Nonlinear multiparameter Sturm–Liouville problems

Article type: Research Article

Authors: Shibata, Tetsutaro^;

Affiliations: Department of Mathematics, Aichi Prefectural University, 3‐28, Takada‐cho, Mizuko‐ku, Nagoya, 467, Japan

Note: [] Present address: The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi‐Hiroshima, 739, Japan. Tel.: +81 (0)824 24 6488; Fax: +81 (0)824 24 0756; E‐mail: [email protected]‐u.ac.jp.

Abstract: An asymptotic formula of variational eigenvalues of nonlinear multiparameter Sturm–Liouville problems is established. The proof is based on Ljusternik–Schnirelman theory on general level sets due to Zeidler, Pohozaev‐type equality and ODE techniques.

Journal: Asymptotic Analysis, vol. 18, no. 3-4, pp. 173-192, 1998