Existence and nonexistence of ground states for a class of quasilinear Schrödinger equations (Q2809502)
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scientific article; zbMATH DE number 6587297
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and nonexistence of ground states for a class of quasilinear Schrödinger equations |
scientific article; zbMATH DE number 6587297 |
Statements
Existence and nonexistence of ground states for a class of quasilinear Schrödinger equations (English)
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30 May 2016
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quasilinear Schrödinger equations
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asymptotically periodic
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three times growth
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Nehari manifold
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ground state
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In this paper, the authors study the following quasilinear Schrödinger equations: NEWLINE\[NEWLINE -\Delta u + V(x)u - u\Delta(u^2) = K(x)u^3, \quad x \in \mathbb{R}^3. NEWLINE\]NEWLINE They assume that \(V\) and \(K\) are suitable perturbations of continuous, \(1\)-periodic maps. They establish the existence and the nonexistence of ground states. The proofs rely on the method of Nehari manifold and the concentration-compactness lemma.
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