Sign-changing solutions for the nonlinear Schrödinger–Poisson system in R3 View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2015-03

AUTHORS

Zhengping Wang, Huan-Song Zhou

ABSTRACT

We are interested in the existence and energy estimate of sign-changing solutions for a Schrödinger–Poisson problem on R3. Because the so-called nonlocal term λϕu(x)u is involving in the equation, the variational functional of the equation has totally different properties from the case of λ=0. By introducing some new ideas, we prove, via a constraint variational method combining the Brouwer degree theory, that the problem has a sign-changing solution under suitable conditions. When λ=0, it is known that any sign-changing solution of the problem has an energy exceeding twice the least energy. However, it is still unknown what would happen when λ>0. We partially answer this question for λ>0 being small. More... »

PAGES

927-943

References to SciGraph publications

  • 2006-01. Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2008-12. On Schrödinger-Poisson Systems in MILAN JOURNAL OF MATHEMATICS
  • 2006-12. Energy bounds for entire nodal solutions of autonomous superlinear equations in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2010-10. On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2008-10. Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2015-08. Non-radial sign-changing solutions for the Schrödinger–Poisson problem in the semiclassical limit in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 1989-09. Uniqueness of positive solutions of Δu−u+up=0 in Rn in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s00526-014-0738-5

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    http://dx.doi.org/10.1007/s00526-014-0738-5

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