Abstract
We consider the nonlinear eigenvalue problem of a nonlinear partial differential equation under Dirichlet boundary condition in a two-dimensional space. The classical solutions are given for rectangular domains. We give numerical solutions obtained by finite element method for the first eigenvalue and eigenfunctions and we analyze the error in the approximate finite element solutions.
References
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[2] G. Bognar. Existence theorem for eigenvalues of a nonlinear eigenvalue problem. Communications on Applied Nonlinear Analysis, 4(2): 93- 102, 1997.
[3] G. Bognar. Error estimates for the finite element solution of a nonlinear elliptic problem. J. of Nonlin. Anal. (to appear)
[4] P.G. Ciarlet. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam- New York- Oxford, 1979.
[5] A. Elbert. A half-linear second order differential equation, Coli. Math. Soc. Janos Bolyai, 30. Qualitative theory of differential equations, 153- 179. Szeged, 1979.
