Ground state solutions for quasilinear Schrodinger equations with periodic potential
Texas State University, Department of Mathematics
This article concerns the quasilinear Schrödinger equation -Δu - uΔ(u2) + V(x)u = K(x)|u|2‧2*-2u + g(x, u), x ∈ ℝN, u ∈ H1(ℝN), u > 0, where V and K are positive, continuous and periodic functions, g(x, u) is periodic in x and has subcritical growth. We use the generalized Nehari manifold approach developed by Szulkin and Weth to study the ground state solution, i.e. the nontrivial solution with least possible energy.
Quasilinear Schrödinger equation, Nehari manifold, Ground state
Zhang, J., & Ji, C. (2020). Ground state solutions for quasilinear Schrodinger equations with periodic potential. <i>Electronic Journal of Differential Equations, 2020</i>(82), pp. 1-12.