Lv, HuilinZheng, ShenzhouFeng, Zhaosheng2022-11-042022-11-042021-12-20Lv, H., Zheng, S., & Feng, Z. (2021). Existence results for nonlinear Schrodinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities. <i>Electronic Journal of Differential Equations, 2021</i>(100), pp. 1-24.1072-6691https://hdl.handle.net/10877/16282In this article, we consider the existence of ground state positive solutions for nonlinear Schrodinger equations of the fractional (p, q)-Laplacian with Rabinowitz potentials defined in ℝn, (-∆)s1pu + (-∆)s2qu + V(εx) (|u|p-2 u + |u|q-2 u) = λƒ(u) + σ|u|q*s2-2 u. We prove existence by confining different ranges of the parameter λ under the subcritical or critical nonlinearities caused by σ = 0 or 1, respectively. In particular, a delicate calculation for the critical growth is provided so as to avoid the failure of a global Palais-Smale condition for the energy functional.Text24 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear Schrödinger equationsNonlocal (p,q)-LaplacianCritical growthRabinowitz potentialsNehari manifoldArticle