FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity |
D. K. Potapov |
2012, issue 1, P. 86–88 |
Abstract |
| We consider the question of existence of Dirichlet’s problem solution for the Laplace equation with a spectral parameter and discontinuous on a phase variable nonlinearity. Using the variational method, we prove a theorem about a number of solutions. We result an example of discontinuous nonlinearity that satisfies to conditions of the theorem for which there is unique semiregular solution of this boundary problem. |
Keywords: Dirichlet’s problem, the Laplace equation, spectral parameter, discontinuous nonlinearity, variational method, number of solutions |
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References |
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