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Perturbation problem for a singular elliptic equation

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We investigate existence and multiplicity of the solutions for the perturbation problem of a singular elliptic equation. We get one theorem which shows existence of at least one nontrivial weak solution under some conditions on which the corresponding functional of the equation satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.

Abstract

We investigate existence and multiplicity of the solutions for the perturbation problem of a singular elliptic equation. We get one theorem which shows existence of at least one nontrivial weak solution under some conditions on which the corresponding functional of the equation satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.

참고문헌 (6)

  1. C. O. Alves, "On systems of equations involving subcritical or critical Sobolev exponents, Nonlinear Analysis", Theory, Meth. and Appl, 42, pp.771~787 (2000)
  2. A. Ambrosetti, "On the inversion of some differential mappings with singularities between Banach spaces", Ann. Mat. Pura. Appl, 93, pp.231~246 (1972)
  3. K. C. Chang, "Ambrosetti-Prodi type results in elliptic systems", Nonlinear Analysis TMA, 51, pp.553~566 (2002)
  4. D. G. de Figueiredo, "Lectures on boundary value problems of the Ambrosetti-Prodi type", 12 Seminario Brasileiro de Analise, pp.232~292 (1980)
  5. M. Ghergu, "Singular elliptic problems Bifurcation and Asymptotic Analysis" (2008), Clarendon Press Oxford
  6. Rabinowitz, P. H., "Minimax methods in critical point theory with applications to differential equations", CBMS. Regional conf. Ser. Math, pp.65~ (1986)

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