Solvability of nonlinear elliptic boundary value problem via its associated linear problem |
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Authors: | Zhi-Qing Han |
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Affiliation: | a Department of Applied Mathematics, Dalian University of Technology, Dalian 116023, Liaoning, PR China b Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China |
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Abstract: | We investigate the existence of solutions of a nonlinear elliptic boundary value problem at resonance. Under the condition that the associated linear boundary value problem has no sign-changing solution or nontrivial solution and some other additional conditions, we prove the existence of solutions or nontrivial (even multiple) solutions to the nonlinear problem. Thus the existence of solutions can be obtained when the nonlinearity may cross any finite number of eigenvalues of the linear problem. |
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Keywords: | Elliptic boundary value problem Eigenvalue Leray-Schauder principle |
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