Weak linking theorems and Schrödinger equations with critical Sobolev exponent

Martin Schechter; Wenming Zou

Displaying similar documents to “Weak linking theorems and Schrödinger equations with critical Sobolev exponent”

Nontrivial solutions of semilinear elliptic systems in $ℝ^{n}$ .

Yang, Jianfu (2001)

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Multiplicity results for positive solutions to non-autonomous elliptic problems.

Qiao, Ning, Wang, Zhi-Qiang (1999)

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Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems.

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An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential.

Spradlin, Gregory S. (2000)

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A positive solution for an asymptotically linear elliptic problem on $ℝ^{N}$ autonomous at infinity

Louis Jeanjean, Kazunaga Tanaka (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on $ℝ^{N}$ . The main difficulties to overcome are the lack of a priori bounds for Palais–Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be...

Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Pedro Girão, Miguel Ramos (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the existence of positive and of nodal solutions for $- Δ u = {| u |}^{p - 2} u + μ {| u |}^{q - 2} u$ , $u \in H_{0}^{1} (Ω)$ , where $μ > 0$ and $2 < q < p = 2 N (N - 2)$ , for a class of open subsets $Ω$ of $ℝ^{N}$ lying between two infinite cylinders.

Multiplicity of solutions for gradient systems using Landesman-Lazer conditions.

da Silva, Edcarlos D. (2010)

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Multiple solutions of a Schrödinger type semilinear equation

Xiaochun Liu, Jianfu Yang (2000)

Commentationes Mathematicae Universitatis Carolinae

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Two nontrivial solutions are obtained for nonhomogeneous semilinear Schrödinger equations.