Journal
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume 12, Issue 2, Pages 867-879Publisher
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/cpaa.2013.12.867
Keywords
Schrodinger-Poisson equations; variational methods; mountain pass
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Funding
- M.I.U.R. - P.R.I.N. Metodi variazionali e topologici nello studio di fenomeni non lineari
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In this paper we study the boundary value problem {-Delta u + epsilon q Phi f(u) = eta vertical bar u vertical bar p(-1)u in Omega, -Delta Phi = 2qF(u) in Omega, u = Phi = 0 on partial derivative Omega, where Omega C R-3 is a smooth bounded domain, 1 < p < 5, epsilon, n = +/- 1, q > 0, f : R -> R is a continuous function and F is the primitive of f such that F(0) = 0. We provide existence and multiplicity results assuming on f a sub-critical growth condition. The critical case is also considered and existence and nonexistence results are proved.
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