Unbalanced fractional elliptic problems with exponential nonlinearity: subcritical and critical cases - Kumar, Deepak; Rădulescu, Vicenţiu D.; Sreenadh, Konijeti (Topological Methods in Nonlinear Analysis, 2022)
This paper deals with the qualitative analysis of solutions to the following (p,q)-fractional equation: equation* (-Δ)^s_1_pu+(-Δ)^s_2_qu+V(x) (|u|^p-2u+|u|^q-2u) = K(x)f(u)|x|^ in R^N, equation* where 1< q< p, 0< s_2≤ s_1< 1, ps_1=N, [0,N), and V,KR^N→R, fR→ R are continuous functions satisfying some natural hypotheses. We are concerned both with the case when f has a subcritical growth and with the critical framework with respect to the exponential nonlinearity. By combining a Moser-Trudinger type inequality for fractional Sobolev spaces with Schwarz symmetrization techniques and related variational and topological methods, we prove the existence of nonnegative solutions.