Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth
Nyckelord:
Critical exponential growth, fractional p-Laplace, Ljusternik-Schnirelmann theory, Mountain Pass Theorem, Trudinger-Moser inequality, variational methodAbstract
In this paper, we study the Schrödinger equation involving \(\frac{N}{s}\)-fractional Laplace as follows \(\varepsilon^{N}(-\Delta)_{N/s}^{s}u+V(x)|u|^{\frac{N}{s}-2}u=f(u)\) in \(\mathbb R^{N}\), where \(\varepsilon\) is a positive parameter, \(N=ps\), \(s\in (0,1)\). The nonlinear function \(f\) has the exponential growth and potential function \(V\) is a continuous function satisfying some suitable conditions. Our problem lacks of compactness. By using the Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter.
Referera så här
Thin, N. V. (2022). Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth. Annales Fennici Mathematici, 47(2), 603–639. https://doi.org/10.54330/afm.115564
Copyright (c) 2022 Annales Fennici Mathematici
Detta verk är licensierat under en Creative Commons Erkännande-IckeKommersiell 4.0 Internationell-licens.