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arxiv: 1210.0755 · v2 · pith:XSSBWJGGnew · submitted 2012-10-02 · 🧮 math.AP

On fractional Schr\"odinger equations in (mathbb{R}^N) without the Ambrosetti-Rabinowitz condition

classification 🧮 math.AP
keywords equationfractionalambrosetti-rabinowitzconditionmathbbodingerschrapproach
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In this note we prove the existence of radially symmetric solutions for a class of fractional Schr\"odinger equation in (\mathbb{R}^N) of the form {equation*} \slap u + V(x) u = g(u), {equation*} where the nonlinearity $g$ does not satisfy the usual Ambrosetti-Rabinowitz condition. Our approach is variational in nature, and leans on a Pohozaev identity for the fractional laplacian.

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