학술저널
MULTIPLE SOLUTIONS FOR THE SYSTEM OF NONLINEAR BIHARMONIC EQUATIONS WITH
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 20, No. 4
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2007.12551 - 560 (10 pages)
- 0
We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condi- tion ½¡¢2u ¡ c¢u + °(bu+ ¡ av¡) = sÁ1 in ;¡¢2v ¡ c¢v + ±(bu+ ¡ av¡) = sÁ1 in ;where u+ = maxfu; 0g, ¢2 denotes the biharmonic operator and Á1 is the positive eigenfunction of the eigenvalue problem ¡¢ with Dirichlet boundary condition.
1. Introduction
2. Nonlinearity crosses the ¯rst eigenvalue
3. Nonlinearity crosses two eigenvalues
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