Solutions for singular critical growth Schrödinger equations with magnetic field.

Han, Pigong

Displaying similar documents to “Solutions for singular critical growth Schrödinger equations with magnetic field.”

A class of $p$ - $q$ -Laplacian type equation with potentials eigenvalue problem in $ℝ^{N}$ .

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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...

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N. Ghoussoub, X. S. Kang (2004)

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Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations.

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Multiple semiclassical solutions of the Schrödinger equation involving a critical Sobolev exponent.

Chabrowski, J., Yang, Jianfu (2000)

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Standing wave solutions of Schrödinger systems with discontinuous nonlinearity in anisotropic media.

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A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

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Let $Ω$ be a bounded open subset of $ℝ^{n}$ , $n > 2$ . In $Ω$ we deduce the global differentiability result $u \in H^{2} (Ω, ℝ^{N})$ for the solutions $u \in H^{1} (Ω, ℝ^{n})$ of the Dirichlet problem $u - g \in H_{0}^{1} (Ω, ℝ^{N}), - \sum_{i} D_{i} a^{i} (x, u, D u) = B_{0} (x, u, D u)$ with controlled growth and nonlinearity $q = 2$ . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.