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On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems

On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value... In this paper we shall consider the nonresonance Dirichlet boundary value problem $$ \left\{ {\begin{array}{*{20}l} {{ - {x}\ifmmode{''}\else$''$\fi + pp{\left( t \right)}x = \lambda f{\left( {t,x} \right)},} \hfill} & {{t \in {\left( {0,1} \right)},} \hfill} \\ {{x{\left( 0 \right)} = x{\left( 1 \right)} = 0,} \hfill} & {{} \hfill} \\ \end{array} } \right. $$ where λ>0 is a parameter, p>0 is a constant. Intervals of λ are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems

Acta Mathematicae Applicatae Sinica , Volume 18 (4) – Jan 1, 2002

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s102550200059
Publisher site
See Article on Publisher Site

Abstract

In this paper we shall consider the nonresonance Dirichlet boundary value problem $$ \left\{ {\begin{array}{*{20}l} {{ - {x}\ifmmode{''}\else$''$\fi + pp{\left( t \right)}x = \lambda f{\left( {t,x} \right)},} \hfill} & {{t \in {\left( {0,1} \right)},} \hfill} \\ {{x{\left( 0 \right)} = x{\left( 1 \right)} = 0,} \hfill} & {{} \hfill} \\ \end{array} } \right. $$ where λ>0 is a parameter, p>0 is a constant. Intervals of λ are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2002

References