JournalsaihpcVol. 29, No. 5pp. 783–812

Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls

  • Norihisa Ikoma

    Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai-Shi, Miyagi 980-8578, Japan

  • Hitoshi Ishii

    Department of Mathematics, Faculty of Education and Integrated Arts and Sciences, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan, Department of Mathematics, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia
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Abstract

We study the eigenvalue problem for positively homogeneous, of degree one, elliptic ODE on finite intervals and PDE on balls. We establish the existence and completeness results for principal and higher eigenpairs, i.e., pairs of an eigenvalue and its corresponding eigenfunction.

Cite this article

Norihisa Ikoma, Hitoshi Ishii, Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 5, pp. 783–812

DOI 10.1016/J.ANIHPC.2012.04.004