Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity

By Xiaojun Chang, Zhi-Qiang Wang. 2013

323 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0b97fb1090be80bed70aef0c57badccdbe76350f

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity (2015, background): “Under (H1)–(H4), ChangandWang [12] proved the existenceof ground state solutions to (1.”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “The literature on fractional operators and their applications is very huge, here we just mention a few, see for example [10–20], especially [21] and [22,23] for two different fractional Laplacian involving concave–convex nonlinearities.”
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, background): “For standing wave solutions of fractional Schrödinger equations in RN , see, for instance, [11, 16] and the references therein.”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, background): “we refer the reader to [3,4,9,10,39] and the references therein.”
Existence of solutions for perturbed fractional p-Laplacian equations (2016, background): “3) For standing wave solutions of fractional Schrödinger equations in R , we refer to [11,14,16, 20,21,26] and the references therein.”
Elliptic problems involving the fractional Laplacian in RN (2013, background): “[13,14,19,22,27,28,32] and for suggesting improvements of the presentation.”
A multiplicity result for a fractional Kirchhoff equation in ℝN with a general nonlinearity (2016, background): “[14] Let (X, ‖ · ‖) be a Banach space such that X is embedded respectively continuously and compactly into L(R ) for q ∈ [q1, q2] and q ∈ (q1, q2), where q1, q2 ∈ (0,∞).”
Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials (2016, methodology): “As a matter of fact, the literature on fractional operators and their applications to partially differential equations is quite large, here we would like to mention a few, see for instance [2, 11, 12, 26, 27, 35].”
Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth (2017, unknown): “See for example [12, 13, 22, 23, 28, 37].”