Geodesic
On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 86-88 
D. K. Potapov. On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 86-88. http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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