Positive solutions for some non-autonomous Schrödinger–Poisson systems
Giovanna Cerami,Giusi Vaira +1 more
TLDR
In this article, the existence of positive solutions for the Schrodinger-Poisson system with nonnegative functions has been proved, but not requiring any symmetry property on them and satisfying suitable assumptions.About:
This article is published in Journal of Differential Equations.The article was published on 2010-02-01 and is currently open access. It has received 306 citations till now.read more
Citations
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Existence and concentration of solutions for the Schrödinger-Poisson equations with steep well potential
TL;DR: In this paper, the existence of nontrivial solution and concentration results are obtained via variational methods under suitable assumptions on V and K. In particular, the potential V is allowed to be sign-changing for the case p ∈ ( 4, 6 ).
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Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains
TL;DR: In this paper, the existence of least energy nodal solution for a class of Schrodinger-Poisson systems with nonlinearity having a subcritical growth was proved for a bounded domain.
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Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth
Xiaoming He,Wenming Zou +1 more
TL;DR: In this paper, the existence and concentration behavior of ground state solutions for a class of Schrodinger-Poisson equation with a parameter ǫ > 0 was studied under some suitable conditions on the nonlinearity f and the potential V in the semi-classical limit.
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Fractional Schrödinger-Poisson Systems with a General Subcritical or Critical Nonlinearity
TL;DR: In this article, a fractional Schrodinger-Poisson system with a general nonlinearity in the subcritical and critical case is considered, and the existence of positive solutions is proved by using a perturbation approach.
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Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials
Xianhua Tang,Sitong Chen +1 more
TL;DR: In this article, Sun et al. studied the Schrodinger-Poisson problem and proved that ground state solutions admit a ground state solution of Nehari-Pohozaev type and a least energy solution under mild assumptions.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Symmetry and related properties via the maximum principle
TL;DR: In this paper, the authors show that positive solutions of second order elliptic equations are symmetric about the limiting plane, and that the solution is symmetric in bounded domains and in the entire space.
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On the variational principle
TL;DR: The variational principle states that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F'(uJj* < l, i.e., its derivative can be made arbitrarily small as discussed by the authors.
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A relation between pointwise convergence of functions and convergence of functionals
TL;DR: In this article, it was shown that if f n is a sequence of uniformly L p-bounded functions on a measure space, and f n → f pointwise a, then lim for all 0 < p < ∞.