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Multiple Solutions for Asymptotically Linear Fractional Schrödinger Equation with Steep Potential Well(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2023年01期
Page:
1-5
Research Field:
数学
Publishing date:

Info

Title:
Multiple Solutions for Asymptotically Linear Fractional Schrödinger Equation with Steep Potential Well
Author(s):
Lu Weidong; Shan Yuan
(School of Mathematics of Nanjing Audit University, Nanjing 211815, China)
Keywords:
fractional Schrö; dinger equation;  steep potential well;  asymptotically linear condition;  multiple solutions
PACS:
O177.91
DOI:
10.3969/j.issn.1001-4616.2023.01.001
Abstract:
In this paper, we study the nonlinear fractional Schrödinger equation (-Δ)su+Vλ(x)u=f(x,u), 0<s<1, x∈RN, on the whole space RN with N>2s. The nonlinearity f is assumed to be asymptotically linear and the potential Vλ has a steep potential well for sufficiently large parameter λ. By virtue of critical point theory, the existence of multiple solutions are obtained.

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Last Update: 2023-03-15