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The method of Nehari manifold
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 findingExpand
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Ground state solutions for some indefinite variational problems
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 bothExpand
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Partial symmetry of least energy nodal solutions to some variational problems
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 ofExpand
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Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
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 nonnegativeExpand
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Multiple solutions of a critical polyharmonic equation
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 DingExpand
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Nodal solutions of a p-Laplacian equation
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 thatExpand
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A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
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
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Three nodal solutions of singularly perturbed elliptic equations on domains without topology
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 . TheExpand
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A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system
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 , inExpand
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