منابع مشابه
Eigenvalues of the p-Laplacian in RN with indefinite weight
We consider the nonlinear eigenvalue problem − div(|∇u|∇u) = λg(x)|u|u in R with p > 1. A condition on indefinite weight function g is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in W (R ). A nonexistence result is also given for the case p ≥ N .
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Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spaces L with the usual norms. Another is the continuity of eigenvalues in weights wi...
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In this article, we study the existence of infinitely many nontrivial solutions for a class of superlinear p-Laplacian equations −∆pu+ V (x)|u| p−2 u = f(x, u), where the primitive of the nonlinearity f is of subcritical growth near ∞ in u and the weight function V is allowed to be sign-changing. Our results extend the recent results of Zhang and Xu [Q. Y. Zhang, B. Xu, Multiplicity of solution...
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The research is financed by the Natural Science Foundation of China and the National Natural Science Foundation of Neimongo. No. 10661008 and 200711020102 (Sponsoring information) Abstract In this paper, we consider an indefinite Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In an appropriate space K, we define a new self-adjoint operato...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-10850-5