Geodesic
Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides
Sbornik. Mathematics, Tome 208 (2017) no. 1, pp. 157-172

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The question on the existence of solutions to eigenvalue problems is treated for nonlinear equations with discontinuous operators in a real Hilbert space. Using a variational method, theorems on the existence of two nontrivial solutions for sufficiently large values of the spectral parameter are proved. As an application, eigenvalue problems for elliptic-type equations with nonlinear terms which are discontinuous in the phase variable are investigated. Bibliography: 22 titles.
Keywords: eigenvalue problems, discontinuous right-hand side, variational method, nontrivial solution. 
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V. N. Pavlenko; D. K. Potapov. Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides. Sbornik. Mathematics, Tome 208 (2017) no. 1, pp. 157-172. http://geodesic.mathdoc.fr/item/SM_2017_208_1_a6/