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

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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].

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Authors and Affiliations

  1. Department of Mathematics, Qufu Normal University, Qufu, 273165, China

    Zhao-cai Hao

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  1. Zhao-cai Hao
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Correspondence to Zhao-cai Hao.

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Supported by the National Natural Science Foundation of China (No. 19871048) and Natural Science Foundation of Shandong Province of China (No. Z2000A02, Y2001A03).

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Hao, Zc. On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems. Acta Mathematicae Applicatae Sinica, English Series 18, 569–578 (2002). https://doi.org/10.1007/s102550200059

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