Far Eastern Mathematical Journal

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On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity


D. K. Potapov

2012, issue 1, Ń. 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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