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Publications Influence

The method of Nehari manifold

- A. Szulkin, T. Weth
- Mathematics
- 2010

We present a unified approach to the method of Nehari manifold for functionals which have a local minimum at 0 and we give several examples where this method is applied to the problem of finding… Expand

195 38- PDF

Ground state solutions for some indefinite variational problems

- A. Szulkin, T. Weth
- Mathematics
- 15 December 2009

Abstract We consider the nonlinear stationary Schrodinger equation − Δ u + V ( x ) u = f ( x , u ) in R N . Here f is a superlinear, subcritical nonlinearity, and we mainly study the case where both… Expand

295 33

Partial symmetry of least energy nodal solutions to some variational problems

- T. Bartsch, T. Weth, M. Willem
- Mathematics
- 1 December 2005

We investigate the symmetry properties of several radially symmetric minimization problems. The minimizers which we obtain are nodal solutions of superlinear elliptic problems, or eigenfunctions of… Expand

167 14- PDF

Dual variational methods and nonvanishing for the nonlinear Helmholtz equation

- Gilles Ev'equoz, T. Weth
- Mathematics
- 12 February 2014

We set up a dual variational framework to detect real standing wave solutions of the nonlinear Helmholtz equation
−Δu−k2u=Q(x)|u|p−2u,u∈W2,p(RN)
with N≥3, 2(N+1)(N−1)<p<2NN−2 and nonnegative… Expand

30 11- PDF

Multiple solutions of a critical polyharmonic equation

- T. Bartsch, M. Schneider, T. Weth
- Mathematics
- 7 January 2004

We prove that for N > 2m the equation (−∆)mu = |u| 4m N−2mu on RN has a sequence of nodal, finite energy solutions which is unbounded in Dm,2(RN ). This generalizes a classical result of Weiyue Ding… Expand

33 10

Nodal solutions of a p-Laplacian equation

- T. Bartsch, Z. Liu, T. Weth
- Mathematics
- 1 July 2005

We prove that the $p$-Laplacian problem $-\Delta_p u = f(x, u)$, with $u \in W^{1, p}_0 (\Omega)$ on a bounded domain $\Omega \subset R^N$, with $p > 1$ arbitrary, has a nodal solution provided that… Expand

103 9

A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems

- W. Reichel, T. Weth
- Mathematics
- 18 September 2007

We consider the 2m-th order elliptic boundary value problem Lu = f (x, u) on a bounded smooth domain $${\Omega\subset\mathbb R^N}$$ with Dirichlet boundary conditions $${u=… Expand

49 9- PDF

Three nodal solutions of singularly perturbed elliptic equations on domains without topology

- T. Bartsch, T. Weth
- Mathematics
- 1 May 2005

Abstract We prove the existence of three nodal solutions of the Dirichlet problem for the singularly perturbed equation − ɛ Δ u + u = f ( u ) for ɛ > 0 small on any bounded domain Ω ⊂ R N . The… Expand

132 8

A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system

- E. N. Dancer, J. Wei, T. Weth
- Mathematics
- 1 May 2010

Abstract We study the set of solutions of the nonlinear elliptic system (P) { − Δ u + λ 1 u = μ 1 u 3 + β v 2 u in Ω , − Δ v + λ 2 v = μ 2 v 3 + β u 2 v in Ω , u , v > 0 in Ω , u = v = 0 on ∂ Ω , in… Expand

159 7- PDF