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

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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. 
@article{DVMG_2012_12_1_a6,
     author = {D. K. Potapov},
     title = {On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {86--88},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a6/}
}
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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/