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On a boundary-value problem with discontinuous solutions and strong nonlinearity
D. A. Chechin, A. D. Baev, S. A. Shabrov Voronezh State University
Abstract:
In this work, sufficient conditions for the existence of a solution to a second-order boundary-value problem with discontinuous solutions and strong nonlinearity are obtained. For the analysis of solutions to the boundary-value problem, we apply the pointwise approach proposed by Yu. V. Pokornyi and which has shown its effectiveness in studying second-order problems with nonsmooth solutions. Based on estimates of the Green function of the boundary-value problem obtained earlier by other authors, we show that the operator, which inverts the nonlinear problem considered, can be represented as the composition of a completely continuous operator and a continuous operator; this operator acts from the cone of nonnegative continuous functions into a narrower set. This fact allows one to prove the existence of a solution to a nonlinear boundary-value problem by using the theory of spaces with a cone.
Keywords:
boundary-value problem, nonsmooth solution, strong nonlinearity, solvability.
Citation:
D. A. Chechin, A. D. Baev, S. A. Shabrov, “On a boundary-value problem with discontinuous solutions and strong nonlinearity”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 153–157
Linking options:
https://www.mathnet.ru/eng/into809 https://www.mathnet.ru/eng/into/v193/p153
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Abstract page: | 122 | Full-text PDF : | 59 | References: | 17 |
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