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In this paper, we study the following critical fractional Schrodinger equation: (−Δ)su+V(x)u=|u|2s*−2u+λf(x,u), x∈RN, where λ > 0, 0 2s, 2s*=2NN−2s, (−Δ)s denotes the fractional Laplacian of order s, and f is… Click to show full abstract
In this paper, we study the following critical fractional Schrodinger equation: (−Δ)su+V(x)u=|u|2s*−2u+λf(x,u), x∈RN, where λ > 0, 0 2s, 2s*=2NN−2s, (−Δ)s denotes the fractional Laplacian of order s, and f is a continuous superlinear but subcritical function. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by the Nehari method.In this paper, we study the following critical fractional Schrodinger equation: (−Δ)su+V(x)u=|u|2s*−2u+λf(x,u), x∈RN, where λ > 0, 0 2s, 2s*=2NN−2s, (−Δ)s denotes the fractional Laplacian of order s, and f is a continuous superlinear but subcritical function. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by the Nehari method.
Journal Title: Journal of Mathematical Physics
Year Published: 2018
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