Abstract
In this paper, we investigate a class of nonlinear fractional Schrödinger systems {(−△)su+V(x)u=Fu(x,u,v),x∈RN,(−△)sv+V(x)v=Fv(x,u,v),x∈RN,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\left \\{ \\textstyle\\begin{array}{l@{\\quad}l}(-\\triangle)^{s} u +V(x)u=F_{u}(x,u,v),& x\\in \\mathbb{R}^{N}, \\\\(-\\triangle)^{s} v +V(x)v=F_{v}(x,u,v),& x\\in\\mathbb{R}^{N}, \\end{array}\\displaystyle \\right . $$\\end{document} where sin(0, 1), N>2. Under relaxed assumptions on V(x) and F(x, u, v), we show the existence of infinitely many high energy solutions to the above fractional Schrödinger systems by a variant fountain theorem.
Highlights
In the work, we are concerned with the existence of infinitely many high energy solutions for the following fractional Schrödinger systems:(– )su + V (x)u = Fu(x, u, v), x ∈ RN,(– )sv + V (x)v = Fv(x, u, v), x ∈ RN, (1.1)where s ∈ (0, 1), N > 2 and Fu(x, u, v), Fv(x, u, v) ∈ C(RN × R × R, R)
In this paper, we investigate a class of nonlinear fractional Schrödinger systems
Under relaxed assumptions on V(x) and F(x, u, v), we show the existence of infinitely many high energy solutions to the above fractional Schrödinger systems by a variant fountain theorem
Summary
Under relaxed assumptions on V(x) and F(x, u, v), we show the existence of infinitely many high energy solutions to the above fractional Schrödinger systems by a variant fountain theorem. 1 Introduction In the work, we are concerned with the existence of infinitely many high energy solutions for the following fractional Schrödinger systems: (– )su + V (x)u = Fu(x, u, v), x ∈ RN , (– )sv + V (x)v = Fv(x, u, v), x ∈ RN , (1.1)
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