Existence of positive solutions to the nonlinear Choquard equation with competing potentials
Texas State University, Department of Mathematics
This article concerns the existence of positive solutions of the non-linear Choquard equation -∆u + α(x)u = b(x) (1/|x| ⁎ |u|2)u, u ∈ H1(ℝ3), where the coefficients α and b are positive functions such that α(x) → κ∞ and b(x) → μ∞ as |x| → ∞. By comparing the decay rate of the coefficients α and b, we prove the existence of positive ground and bound stat solutions of Choquard equation.
Positive solutions, Choquard equation, Competing coefficients, Variational methods
Wang, J., Qu, M., & Xiao, L. (2018). Existence of positive solutions to the nonlinear Choquard equation with competing potentials. <i>Electronic Journal of Differential Equations, 2018</i>(63), pp. 1-21.