Existence results for nonlinear Schrodinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities
Texas State University, Department of Mathematics
In 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.
Nonlinear Schrödinger equations, Nonlocal (p,q)-Laplacian, Critical growth, Rabinowitz potentials, Nehari manifold
Lv, 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.