Publications of Tobias Weth

Preprints are listed here

Accepted and Published Research Papers

[91] A supercritical elliptic equation in the annulus (with A. Boscaggin, F. Colasuonno and B. Noris), to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire

[90] Trudinger-Moser type inequality with logarithmic convolution potentials (with S. Cingolani), to appear in J. London Math. Soc.

[89] Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian (with P.A. Feulefack and S. Jarohs), to appear in J. Fourier Anal. Appl.

[88] A fractional Hadamard formula and applications (with S.M. Djitte and M.M. Fall), Calc. Var. Partial Differential Equations 60, 231 (2021).

[87] Symmetry properties of sign-changing solutions to nonlinear parabolic equations in unbounded domains (with J. Földes and A. Saldana) Journal of Dynamics and Differential Equations (2021),

[86] The Poisson problem for the fractional Hardy operator: Distributional identities and singular solutions (with H. Chen), Trans. Amer. Math. Soc. 374 (2021), 6881-6925.

[85] Spiraling solutions of nonlinear Schrödinger equations (with O. Agudelo and J. Kübler), Proc. Roy. Soc. Edinburgh Sect. A (2021), DOI:

[84] Spectral properties of the logarithmic Laplacian (with A. Laptev), Anal. Math. Phys. 11, 133 (2021).

[83] Nodal solutions for sublinear-type problems with Dirichlet boundary conditions (with D. Bonheure, E. Moreira dos Santos, E. Parini and  H. Tavares), International Mathematics Research Notices (2021), rnaa233,

[82] The nonlinear Schrödinger equation in the half-space (with A. J. Fernández), Math. Ann. (2021),

[81] Morse index versus radial symmetry for fractional Dirichlet problems (with M.M. Fall, P.A. Feulefack, R. Y. Temgoua), Adv. Math. 384 (2021), 107728, 22 pp. 

[80] Complex solutions and stationary scattering for the nonlinear Helmholtz equation (with G. Evéquoz and H. Chen), SIAM J. Math. Anal. 53 (2021), no. 2, 2349-2372.

[79] Fourier extension estimates for symmetric functions and applications to nonlinear Helmholtz equations (with T. Yeşil), Ann. Mat. Pura Appl. 200 (2021), 2423 - 2454,

[78] Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation (with J. Kübler), Discrete Contin. Dyn. Syst. 40 (2020), no. 6, 3629–3656.

[77] A new look at the fractional Poisson problem via the logarithmic Laplacian (with S. Jarohs and A. Saldaña), J. Funct. Anal. 279 (2020), no. 11, 108732.

[76] Local compactness and nonvanishing for weakly singular nonlocal quadratic forms (with S. Jarohs), Nonlinear Anal. 193 (2020), 111431, 15 pp.

[75] The Dirichlet Problem for the Logarithmic Laplacian (with H. Chen),  Comm. Partial Differential Equations 44 (2019), 1100–1139.

[74] Critical domains for the first nonzero Neumann eigenvalue in Riemannian manifolds (w. M.M. Fall),  J. Geom. Anal. 29 (2019), 3221–3247.

[73] Unstable normalized standing waves for the space periodic NLS (with N. Ackermann), Anal. PDE 12 (2019), 1177–1213.

[72] Symmetry breaking via Morse index for equations and systems of Hénon–Schrödinger type (with Z. Lou and Z. Zhang), Z. Angew. Math. Phys. 70 (2019), no. 1, Paper No. 35, 19 pp.

[71] On the strong maximum principle for nonlocal operators (with S. Jarohs), Math. Z. 293 (2019), 81–111. (2018).

[70] Near-sphere lattices with constant nonlocal mean curvature (with X. Cabré and M. M. Fall), Math. Ann. 370 (2018), 1513–1569.

[69]  The unique continuation property of sublinear equations (with N. Soave), SIAM J. Math. Anal. 50 (2018), 3919–3938

[68] Serrin's overdetermined problem on the sphere (with M.M. Fall and I.A. Minlend), Calc. Var. Partial Differential Equations 57 (2018), no. 1, Art. 3, 24 pp.

[67] Delaunay hypersurfaces with constant nonlocal mean curvature (with X. Cabré and M.M. Fall), J. Math. Pures Appl. (9) 110 (2018), 32–70.

[66] Curves and surfaces with constant nonlocal mean curvature: meeting Alexandrov and Delaunay (with X. Cabré, M.M. Fall and J. Solà-Morales), J. Reine Angew. Math. 745 (2018), 253–280.

[65] Ground states and high energy solutions of the planar Schrödinger-Poisson system (with M. Du), Nonlinearity 30 (2017), 3492–3515.

[64] Profile expansion for the first nontrivial Steklov eigenvalue in Riemannian manifolds (with M.M. Fall),  Comm. Anal. Geom. 25 (2017), 431–463.

[63] Unbounded periodic solutions to Serrin's overdetermined boundary value problem (with M.M. Fall and I. Minlend), Arch. Rational Mech. Anal. 223 (2017), 737-759.

[62] Branch continuation inside the essential spectrum for the nonlinear Schrödinger equation (with G. Evéquoz), J. Fixed Point Theory Appl. 19 (2017), 475-502.

[61] Liouville theorems for a general class of nonlocal operators (with M.M. Fall), Potential Anal. 45 (2016), 187–200.

[60] Localized solvability of relaxed one-sided Lipschitz inclusions in Hilbert spaces (with J. Rieger), SIAM J. Optim. 26 (2016), 227-246.

[59] On the planar Schrödinger-Poisson system (with S. Cingolani), Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), 169-197.

[58] Symmetry via antisymmetric maximum principles in nonlocal problems of variable order (with S. Jarohs), Ann. Mat. Pura Appl. 195 (2016), 273-291.

[57] Monotonicity and nonexistence results for some fractional elliptic problems in the half-space (with M.M. Fall), Commun. Contemp. Math. 18 (2016), 1550012, 25 pp.

[56] Dual variational methods and nonvanishing for the nonlinear Helmholtz equation (with G. Evéquoz), Adv. Math. 280 (2015), 690–728.

[55] Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems (with E. Parini),  Math. Z. 280 (2015), no. 3-4, 707–732.

[54] On the Asymptotic Shape of Solutions to Neumann Problems for non-cooperative Parabolic Systems (with A. Saldana), J. Dynam. Differential Equations 27 (2015), no. 2, 307–332.

[53] Asymptotic symmetry for a class of fractional reaction-diffusion equations (with S. Jarohs), Discrete Contin. Dyn. Syst. 34 (2014), 2581–2615.

[52] Real solutions to the nonlinear Helmholtz equation with local nonlinearity (with G. Evéquoz), Arch. Ration. Mech. Anal. 211 (2014), 359-388.

[51] Sharp local estimates for the first non-zero Neumann eigenvalue in Riemannian manifolds (with M. M. Fall), Calc. Var. Partial Differential Equations 51 (2014), 217–242.

[50] Remainder terms in the fractional Sobolev inequality (with S. Chen and R.L. Frank),  Indiana Univ. Math. J. 62 (2013), 1381–1397.

[49] Existence and symmetry results for competing variational systems (with H. Tavares), Nonlinear. Differ. Equ. Appl. 20  (2013), 715–740.

[48] Nonexistence results for a class of fractional elliptic boundary value problems (with  M.M. Fall), J. Funct. Anal.  263  (2012),  no. 8, 2205–2227.

[47] Increasing radial solutions for Neumann problems without growth restrictions (with D. Bonheure and B. Noris), Ann. Inst. H. Poincaré Anal. Non Linéaire  29  (2012), 573–588.

[46] Asymptotic axial symmetry of solutions of parabolic  equations in bounded radial domains (with A. Saldana), J. Evolution Equations 12  (2012), 697–712. 

[45] Entire solutions to nonlinear scalar field equations with indefinite linear part (with G. Evéquoz), Adv. Nonlinear Studies  12  (2012), 281–314.

[44] Liouville Type results for noncooperative elliptic systems in a half space (with E.N. Dancer), J. London Math. Soc. (2) 86 (2012) 111–128.

[43] On the lack of directional quasiconcavity of the fundamental mode in the clamped membrane problem. Arch. Math 97 (2011), 365-372.

[42] Existence and nonexistence of entire solutions for non-cooperative elliptic systems (with H. Tavares, S. Terracini and G. Verzini). Comm. Partial Differential Equations 36  (2011),  no. 11, 1988–2010.

[41] Remainder terms in a higher order Sobolev inequality (with F. Gazzola). Arch. Math. 95 (2010), 381-388.

[40] N-vortex equilibria for ideal fluids in bounded planar domains and N-solitons for the sinh-Poisson equation (with T. Bartsch and A. Pistoia). Comm. Math. Phys. 297 (2010), 653-686.

[39] A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system (with E.N. Dancer and J.C. Wei). Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 953-969.

[38] Existence of solutions to nonlinear subcritical higher order elliptic Dirichlet problems (with W. Reichel). J. Differential Equations 248 (2010), 1866–1878.

[37] Symmetry and nonexistence of low Morse index solutions in unbounded domains (with F. Gladiali and F. Pacella)   J. Math. Pures Appl. 93 (2010), 536–558.

[36] Ground state solutions for some indefinite variational problems (with A. Szulkin).  J. Funct. Anal. 257 (2009),  3802-3822.

[35] Ground state solutions for a semilinear problem with a critical exponent (with A. Szulkin and M. Willem). Differential Integral Equations 22 (2009), 913-926.

[34] A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems (with W. Reichel). Math. Z. 261 (2009), 805-827.

[33] Radial symmetry of positive solutions to nonlinear polyharmonic Dirichlet problems (with E. Berchio und F. Gazzola). J. Reine Angew. Math. 620 (2008), 165–183.

[32] Radial solutions and phase separation in a system of two coupled Schrödinger equations (with J.C. Wei). Arch. Rational Mech. Anal. 190 (2008), 83–106.

[31] Asymptotic behavior of solutions of planar elliptic systems with strong competition (mit J.C. Wei). Nonlinearity 21 (2008), 305-317.

[30] Two solutions of the Bahri-Coron problem in punctured domains via the fixed point transfer (with M. Clapp). Commun. Contemp. Math. 10 (2008), 81-101.

[29] Nonradial symmetric bound states for a system of coupled Schrödinger equations (with J.C. Wei) Rend. Lincei Mat. Appl 18 (2007), 279-294.

[28] Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
(with A. Pistoia). Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), 325-340.

[27] Symmetry of solutions to semilinear elliptic equations via Morse index (with F. Pacella). Proc. Amer. Math. Soc. 135 (2007), 1753-1762.

[26] Critical growth biharmonic elliptic problems under Steklov-type boundary conditions (with E. Berchio and F. Gazzola) Adv. Differential Equations 12 (2007), 381-406.

[25] Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation (with T. Bartsch und M. Clapp) Math. Ann. 338 (2007) 147-185.

[24] Positivity, symmetry and uniqueness for minimizers of second order Sobolev inequalities (with A. Ferrero and F. Gazzola). Ann. Mat. Pura Appl. 186 (2007), 565-578.

[23] Compactness results for Schrödinger equations with asymptotically linear terms (with Z.L. Liu and J.B. Su). J. Differential Equations 231 (2006), 501-512.

[22] Nodal solutions to superlinear biharmonic equations via decomposition in dual cones. Topol. Methods Nonlinear Anal. 28 (2006), 33-52.

[21] Energy bounds for entire nodal solutions of autonomous superlinear equations. Calc. Var. Partial Differential Equations 27 (2006), 421-437

[20] The shape of extremal functions for Poincare-Sobolev-type inequalities in a ball (with P. Girao). J. Funct. Anal. 237 (2006), 194-223.

[19] Multiple solutions of nonlinear Schrödinger equations via flow invariance and Morse theory
          (with Z.L. Liu and Z.Q. Wang). Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), 945-969.

[18] A spectral theoretic approach to semilinear eigenvalue problems. Mitt. Math. Sem. Giessen 258 (2006), 1-68.

[17] On the number of nodal solutions to a singularly perturbed Neumann problem (with J.C. Wei). manuscripta math. 117 (2005), 333-344.

[16] Partial symmetry of least energy nodal solutions to some variational problems (with T. Bartsch and M. Willem). J. Anal. Math. 96 (2005), 1-18.

[15] The effect of the domain’s configuration space on the number of nodal solutions of singularly perturbed elliptic equations (with T. Bartsch). Topol. Methods Nonlinear Anal. 26 (2005), 109-134.

[14] Finite time blow up and global solutions for semilinear parabolic equations with initial data at high energy level (with F. Gazzola). Differential Integral Equations 18 (2005), 961-990.

[13] Multibump solutions to nonlinear periodic Schrödinger equations in a degenerate setting (with N. Ackermann). Commun. Contemp. Math. 7 (2005), 269–298.

[12] Nodal solutions of a p-Laplacian equation (with T. Bartsch and Z.L. Liu). Proc. London Math. Soc. (3) 91 (2005), 129–152.

[11] Global bifurcation branches for superlinear Schrödinger equations. Adv. Differential Equations 10 (2005), 721–746.

[10] Multiple solutions for the Brezis-Nirenberg problem (with M.Clapp). Adv. Differential Equations 10 (2005), 463-480.

[9] Three nodal solutions of singular perturbed equations on domains without topology (with T. Bartsch). Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), 259-281.

[8] On a fourth order Steklov eigenvalue problem (with A. Ferrero and F. Gazzola) Analysis 25 (2005), 315-332.

[7] Multiple solutions of nonlinear scalar field equations (with M. Clapp). Comm. Partial Differential Equations 29 (2004), 1533-1554.

[6] Minimal nodal solutions of the pure critical exponent problem on a symmetric domain (with M. Clapp). Calc. Var. Partial Differential Equations 21 (2004), 1-14.

[5] Multiple solutions to a critical polyharmonic equation (with T. Bartsch and M. Schneider). J. Reine Angew. Math. 571 (2004), 131–143.

[4] Sign changing solutions to superlinear Schrödinger equations (with T. Bartsch and Z.L. Liu). Comm. Partial Differential Equations 29 (2004), 25-42.

[3] A note on additional properties of sign changing solutions to superlinear elliptic equations (with T. Bartsch). Topol. Methods Nonlinear Anal. 22 (2003), 1-14.

[2] A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator (with T. Bartsch and M. Willem). Calc. Var. Partial Differential Equations 18 (2003), 253-268

[1] Nonlinear Eigenvalue Problems of Schrödinger Type Admitting Eigenfunctions with Given Spectral Characteristics (with M. Heid and H.P. Heinz). Math. Nachr. 242 (2002), 91-118.

Survey articles

[1] Symmetry of solutions to variational problems for nonlinear elliptic equations via reflection methods. Jahresber. Deutsch. Math.-Ver. 112 (2010), 119-158

[2] The method of Nehari manifold (with A. Szulkin), in: Handbook of Nonconvex Analysis and Applications, D.Y. Gao and D. Motreanu eds., International Press, Boston, 2010, pp. 597-632.

Conference Proceedings

[4] Liouville type theorems for a class of non-cooperative elliptic systems. Oberwolfach Reports 6 (2009), 1473-1475.

[3] Partial symmetry of solutions to semilinear elliptic equations via Morse index estimates. Oberwolfach Reports 5 (2009), 1748-1749.

[2] Energy bounds for entire nodal solutions of autonomous elliptic equations via the moving plane method. Abstracts from the workshop held June 26–July 2, 2005. Organized by T. Bartsch and E.N. Dancer. Oberwolfach Reports 2 (2005), 1601-1678.

[1] Sign changing solutions of superlinear Schr¨odinger equations, in: Topological methods, variational methods and their applications (Taiyuan, 2002), 249–257, World Sci. Publishing, River Edge, NJ, 2003.


 [1]    Erratum to: N-vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh-Poisson and the Lane-Emden-Fowler equations  (with T. Bartsch and A. Pistoia). Comm. Math. Phys. 333 (2015), 1107.


Spectral and variational characterizations of solutions to semilinear eigenvalue problems.

Dissertation, Universität Mainz (2001)

A shortened version is published in Mitt. Math. Sem. Giessen, see [18]


Habilitation Thesis

On the number and shape of solutions to some semilinear elliptic equations.

Universität Giessen (2007)