Topic
Dirichlet eigenvalue
About: Dirichlet eigenvalue is a research topic. Over the lifetime, 1912 publications have been published within this topic receiving 31564 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: On etudie le probleme de Dirichlet dans un domaine borne Ω de R n a frontiere lisse ∂Ω:F(D 2 u)=ψ dans Ω, u=φ sur ∂ Ω as discussed by the authors.
Abstract: On etudie le probleme de Dirichlet dans un domaine borne Ω de R n a frontiere lisse ∂Ω:F(D 2 u)=ψ dans Ω, u=φ sur ∂Ω
1,064 citations
Book•
18 Jul 2006TL;DR: The first eigenvalue of the Laplacian-Dirichlet operator was defined in this paper and the other Dirichlet eigenvalues were defined in this paper.
Abstract: Eigenvalues of elliptic operators.- Tools.- The first eigenvalue of the Laplacian-Dirichlet.- The second eigenvalue of the Laplacian-Dirichlet.- The other Dirichlet eigenvalues.- Functions of Dirichlet eigenvalues.- Other boundary conditions for the Laplacian.- Eigenvalues of Schrodinger operators.- Non-homogeneous strings and membranes.- Optimal conductivity.- The bi-Laplacian operator.
998 citations
Book•
31 Oct 2000TL;DR: The Dirichlet problem for strongly elliptic systems in particular cones has been studied in this paper, where the authors show that the spectrum of operator pencils generated by general boundary value problems in an angle is a function of the singularities of the solution.
Abstract: Introduction Singularities of solutions to equations of mathematical physics: Prerequisites on operator pencils Angle and conic singularities of harmonic functions The Dirichlet problem for the Lame system Other boundary value problems for the Lame system The Dirichlet problem for the Stokes system Other boundary value problems for the Stokes system in a cone The Dirichlet problem for the biharmonic and polyharmonic equations Singularities of solutions to general elliptic equations and systems: The Dirichlet problem for elliptic equations and systems in an angle Asymptotics of the spectrum of operator pencils generated by general boundary value problems in an angle The Dirichlet problem for strongly elliptic systems in particular cones The Dirichlet problem in a cone The Neumann problem in a cone Bibliography Index List of symbols.
505 citations
373 citations
TL;DR: In this article, it was shown that when the derivative of the nonlinearity at zero is less than the first eigenvalue of with zero Dirichlet boundry condition, there still exists a solution which changes sign at most k times.
Abstract: In previous work by Castro, Cossio, and Neuberger [2], it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k +1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k = 1 the sign-changing exactly-once solution persists although one-sign solutions no longer exist.
330 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 7 |
| 2024 | 11 |
| 2023 | 34 |
| 2022 | 34 |
| 2021 | 44 |
| 2020 | 55 |