Existence of infinitely many small solutions for sublinear fractional Kirchhoff-Schrodinger-Poisson systems
Date
2019-01-25
Authors
de Albuquerque, Jose Carlos
Clemente, Rodrigo
Ferraz, Diego
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the Kirchhoff-Schrödinger-Poisson system
m([u]2α) (-Δ)α u + V(x)u + k(x)φu = ƒ(x, u), x ∈ ℝ3,
(-Δ)β φ = k(x)u2, x ∈ ℝ3,
where [∙]α denotes the Gagliardo semi-norm, (-Δ)α denotes the fractional Laplacian operator with α, β ∈ (0, 1], 4α + 2β ≥ 3 and m : [0, +∞) → [0, +∞) is a Kirchhoff function satisfying suitable assumptions. The functions V(x) and k(x) are nonnegative and the nonlinear term ƒ(x, s) satisfies certain local conditions. By using a variational approach, we use a Kajikiya's version of the symmetric mountain pass lemma and Moser iteration method to prove the existence of infinitely many small solutions.
Description
Keywords
Kirchhoff-Schrödinger-Poisson equation, Fractional Laplacian, Variational method
Citation
de Albuquerque, J. C., Clemente, R., & Ferraz, D. (2019). Existence of infinitely many small solutions for sublinear fractional Kirchhoff-Schrodinger-Poisson systems. Electronic Journal of Differential Equations, 2019(13), pp. 1-16.
Rights
Attribution 4.0 International