Ground state solutions for nonlinear fractional Schrödinger equations in RN
By Simone Secchi. 2012
445 citations recorded by the source corpus.
We construct solutions to a class of Schrodinger equations involving the fractional Laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.
Subfields: Applied Mathematics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/012da0039c9335e6c4ca48c6e190e642575315fb
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In Applied Mathematics
- Binlin Zhang
- Mingqi Xiang
- Patrizia Pucci
- Vicentiu D. Rădulescu
- Enrico Valdinoci
- G. Autuori
- A. Fiscella
- Serena Dipierro
In Materials Chemistry
- G. Autuori
- Maicol Caponi
- Manuel del Pino
- J. D'avila
- Enrico Valdinoci
- Mingqi Xiang
- Binlin Zhang
- Patrizia Pucci
Citations in the corpus
- Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum (2014, background): “concentration phenomena in particular cases, and also [Secchi 2013] and references therein for related problems about Schrödinger-type equations in a fractional setting.”
- Concentrating standing waves for the fractional nonlinear Schr\"odinger equation (2013, unknown): “Some results of variational type for 0 < s < 1 have been obtained for instance in [12] and [24].”
- On fractional Schr\"odinger equations in (\mathbb{R}^N) without the Ambrosetti-Rabinowitz condition (2012, unknown): “he literature. In [10] the authors prove the existence of a nontrivial, radially symmetric, solution to the equation (−∆)s u+u =|u|p−1u in RN for subcritical exponents 1 <p <(N +2s)/(N −2s). In [19, 20] the author proves some existence results for fractional Schrödinger equations, under the as”
- Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, background): “Models governedby the fractional p-Laplacian andunboundedpotentials are investigated in [5, 22, 32].”
- The concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system (2017, unknown): “See [8,16,18,31,38,39] for the existence of solutions.”