Electron. J. Diff. Equ., Vol. 2016 (2016), No. 212, pp. 1-12.

Sublinear eigenvalue problems with singular weights related to the critical Hardy inequality

Megumi Sano, Futoshi Takahashi

In this article, we consider a weighted sublinear eigenvalue problem related to an improved critical Hardy inequality. We discuss to what extent the weights can be singular for the existence of weak solutions. Also we study the asymptotic behavior of the first eigenvalues as a parameter involved varies.

Submitted July 8, 2016. Published August 10, 2016.
Math Subject Classifications: 35A23, 35J62, 35J20.
Key Words: Critical Hardy inequality; sublinear reaction term; eigenvalue problem.

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Megumi Sano
Department of Mathematics
Graduate School of Science
Osaka City University,
Sumiyoshi-ku, Osaka, 558-8585, Japan
email: megumisano0609@st.osaka-cu.ac.jp
Futoshi Takahashi
Department of Mathematics
Osaka City University & OCAMI, Sumiyoshi-ku
Osaka, 558-8585, Japan
email: futoshi@sci.osaka-cu.ac.jp

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