Displaying similar documents to “New method for computation of discrete spectrum of radical Schrödinger operator”

Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients

Yu Zhang, Hai Bi, Yidu Yang (2021)

Applications of Mathematics

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In this paper, using a new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain asymptotic lower bounds of eigenvalues for the Steklov eigenvalue problem with variable coefficients on d -dimensional domains ( d = 2 , 3 ). In addition, we prove that the corrected eigenvalues converge to the exact ones from below. The new result removes the conditions of eigenfunction being singular and eigenvalue being large enough, which are usually required in the existing arguments...

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in R N

Lucio Damascelli (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We present a simple proof of the fact that if Ω is a bounded domain in R N , N ≥ 2 , which is convex and symmetric with respect to k orthogonal directions, 1 ≤ k ≤ N , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues λ 2 , ⋯ , λ k + 1 must intersect the boundary. This result was proved by Payne in the case N = 2 for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.

On the existence of five nontrivial solutions for resonant problems with p-Laplacian

Leszek Gasiński, Nikolaos S. Papageorgiou (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of ( - Δ ₚ , W ₀ 1 , p ( Z ) ) . We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.

Eigenvalue problems with indefinite weight

Andrzej Szulkin, Michel Willem (1999)

Studia Mathematica

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We consider the linear eigenvalue problem -Δu = λV(x)u, u ∈ D 0 1 , 2 ( Ω ) , and its nonlinear generalization - Δ p u = λ V ( x ) | u | p - 2 u , u ∈ D 0 1 , p ( Ω ) . The set Ω need not be bounded, in particular, Ω = ℝ N is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues λ n → ∞ .