Ground state, bound states and bifurcation properties for a Schrodinger-Poisson system with critical exponent

Date

2019-02-18

Authors

Chen, Jianqing
Huang, Lirong
Rocha, Eugenio M.

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the existence of ground state and bound states, and the study of their bifurcation properties for the Schrödinger-Poisson system -Δu + u + φu = |u|4u + µh(x)u, -Δφ = u2 in ℝ3. Under suitable assumptions on the coefficient h(x), we prove that the ground state must bifurcate from zero, and that another bound state bifurcates from a solution, when µ = µ1 is the first eigenvalue of -Δu + u = µh(x)u in H1(ℝ3).

Description

Keywords

Ground state and bound states, Bifurcation properties, Schrödinger-Poisson system, Variational method

Citation

Chen, J., Huang, L., & Rocha, E. M. (2019). Ground state, bound states and bifurcation properties for a Schrodinger-Poisson system with critical exponent. <i>Electronic Journal of Differential Equations, 2019</i>(28), pp. 1-23.

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Attribution 4.0 International

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