Geodesic
Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 247-261

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We consider a strongly resonant homogeneous Dirichlet problem for elliptic-type equations with discontinuous nonlinearity in the phase variable. Using the variational method, we prove an existence theorem for at least three nontrivial solutions of the problem under consideration; at least two of these are semiregular. The resulting theorem is applied to the eigenvalue problem for elliptic-type equations with discontinuous nonlinearity with positive spectral parameter. An example of a discontinuous nonlinearity satisfying all the assumptions of the theorem is given.
Keywords: elliptic boundary-value problem, strong resonance, discontinuous nonlinearity, nontrivial and semiregular solution. 
@article{MZM_2017_101_2_a9,
     author = {V. N. Pavlenko and D. K. Potapov},
     title = {Existence of {Three} {Nontrivial} {Solutions} of an {Elliptic} {Boundary-Value} {Problem} with {Discontinuous} {Nonlinearity} in the {Case} of {Strong} {Resonance}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {247--261},
     publisher = {mathdoc},
     volume = {101},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a9/}
}
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V. N. Pavlenko; D. K. Potapov. Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 247-261. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a9/