Journal
ANNALES FENNICI MATHEMATICI
Volume 47, Issue 2, Pages 603-639Publisher
SUOMALAINEN TIEDEAKATEMIA
DOI: 10.54330/afm.115564
Keywords
Critical exponential growth; fractional p-Laplace; Ljusternik-Schnirelmann theory; Mountain Pass Theorem; Trudinger-Moser inequality; variational method
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Funding
- Thai Nguyen University of Education [TNUE-2022-01]
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In this paper, we study the existence, multiplicity, and concentration of nontrivial nonnegative solutions of the Schrödinger equation involving the fractional Laplacian. By using the Ljusternik-Schnirelmann theory, we obtain these results for small values of the parameter.
In this paper, we study the Schrodinger equation involving the Ns-fractional Laplacian: epsilon N(-Delta)sN/su + V (x)|u| Ns -2u = f (u) in RN, where epsilon is a positive parameter, N = ps, s is an element of (0, 1). The nonlinear function f has exponential growth and the potential function V is a continuous function satisfying some suitable conditions. Our problem lacks compactness. By using the Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter.
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