منابع مشابه
Variational eigenvalues of degenerate eigenvalue problems for the weighted p-Laplacian
We prove the existence of nondecreasing sequences of positive eigenvalues of the homogeneous degenerate quasilinear eigenvalue problem − div(a(x)|∇u|p−2∇u) = λb(x)|u|p−2u, λ > 0 with Dirichlet boundary condition on a bounded domain Ω. The diffusion coefficient a(x) is a function in Lloc(Ω) and b(x) is a nontrivial function in L(Ω) (r depending on a, p and N) and may change sign. We use Ljustern...
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In this work we derive oscillation and nonoscillation criteria for the one dimensional p-laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willet, and the proof is based on a Picone type identity.
متن کاملStability of variational eigenvalues for the fractional p–Laplacian
By virtue of Γ−convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional p−Laplacian operator, in the singular limit as the nonlocal operator converges to the p−Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.
متن کاملEigenvalues 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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We also prove that the lower bound is sharp. Eigenvalue problems for quasilinear operators of p-Laplace type like (1.1) have received considerable attention in the last years (see, e.g., [1, 2, 3, 5, 8, 13]). The asymptotic behavior of eigenvalues was obtained in [6, 7]. Lyapunov inequalities have proved to be useful tools in the study of qualitative nature of solutions of ordinary linear diffe...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11742-9