Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2013 · 20 citations · 7 references
Natural SciencesMathematicsPhysicsDifferential EquationsNumber TheoryQuantum MechanicsExistence TheorySchrödinger EquationNonlinear Schrödinger EquationPoisson EquationPoisson's EquationSchrödinger-poisson System
We study the existence and multiplicity of positive solutions for the following nonlinear Schrödinger–Poisson equations: where 2 < p ≤ 3 or 4 ≤ p < 6, λ > 0 and Q ∈ C (ℝ 3 ). We show that the number of positive solutions is dependent on the profile of Q ( x ).
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Ivar Ekeland · Journal of Mathematical Analysis and Applications · 1974 · 2.3K citations · Full text