Ground state, bound states and bifurcation properties for a Schrodinger-Poisson system with critical exponent
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Date
2019-02-18
Authors
Chen, Jianqing
Huang, Lirong
Rocha, Eugenio M.
Journal Title
Journal ISSN
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