2017
Том 69
№ 9

All Issues

Existence Theorem for One Class of Strongly Resonance Boundary-Value Problems of Elliptic Type with Discontinuous Nonlinearities

Chizh E. A., Pavlenko V. N.

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Abstract

We consider the Dirichlet problem for an equation of the elliptic type with a nonlinearity discontinuous with respect to the phase variable in the resonance case; it is not required that the nonlinearity satisfy the Landesman-Lazer condition. Using the regularization of the original equation, we establish the existence of a generalized solution of the problem indicated.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 1, pp 121-131.

Citation Example: Chizh E. A., Pavlenko V. N. Existence Theorem for One Class of Strongly Resonance Boundary-Value Problems of Elliptic Type with Discontinuous Nonlinearities // Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 102–110.

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