School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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In this article we study the Schrödinger-Poisson system−∆ u+ V (| x|) u+ λφu= f (u), x∈ R3,−∆ φ= u2, x∈ R3, where V is a singular potential with the parameter α and the nonlinearity f satisfies critical growth. By applying a generalized version of Lions-type theorem and the Nehari manifold theory, we establish the existence of the nonnegative ground state solution when λ= 0. By the perturbation method, we obtain a nontrivial solution to above system when λ= 0.


Copyright 2020 Texas State University.

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Electronic Journal of Differential Equations

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Mathematics Commons



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