Geodesic
Semiregular solutions of elliptic boundary-value problems with discontinuous nonlinearities of exponential growth
Sbornik. Mathematics, Tome 213 (2022) no. 7, pp. 1004-1019 Cet article a éte moissonné depuis la source Math-Net.Ru

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An elliptic boundary-value problem with discontinuous nonlinearity of exponential growth at infinity is investigated. The existence theorem for a weak semiregular solution of this problem is deduced by the variational method. The semiregularity of a solution means that its values are points of continuity of the nonlinearity with respect to the phase variable almost everywhere in the domain where the boundary-value problem is considered. The variational approach used is based on the concept of a quasipotential operator, unlike the traditional approach, which uses Clarke's generalized derivative. Bibliography: 29 titles.
Keywords: elliptic boundary-value problem, discontinuous nonlinearity, exponential growth, semiregular solution, variational method. 
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V. N. Pavlenko; D. K. Potapov. Semiregular solutions of elliptic boundary-value problems with discontinuous nonlinearities of exponential growth. Sbornik. Mathematics, Tome 213 (2022) no. 7, pp. 1004-1019. http://geodesic.mathdoc.fr/item/SM_2022_213_7_a3/

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