Abstract
In this paper, we study the Schrödinger equation involving the fractional (p,p1)-Laplacian and Trudinger-Moser nonlinearity as follows(−Δ)N/ssu+(−Δ)p1su+V(εx)(|u|Ns−2u+|u|p1−2u)=f(u)inRN, where ε is a positive parameter, N=ps,s∈(0,1),2≤Ns=p<p1. The nonlinear function f has the exponential growth and potential function V is continuous function satisfying some suitable conditions. By using the Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter. In our best knowledge, it is the first time that the fractional (p,p1)-Laplacian problem involving exponential growth is studied.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
