Existence of solutions, estimates for the differential operator, and a “separating” set in a boundary value problem for a second-order differential equation with a discontinuous nonlinearity

We study the existence of solutions of the Sturm–Liouville problem with a nonlinearity discontinuous with respect to the state variable. By the variational method, we prove theorems on the existence of semiregular and regular solutions, estimates for the differential operator, and properties of a “s...

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Bibliographic Details
Published in:Differential equations 2015-07, Vol.51 (7), p.967-972
Main Author: Potapov, D. K.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Estimates
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear systems
Nonlinearity
Operators
Ordinary Differential Equations
Partial Differential Equations
Separated flow
Short Communications
Studies
Variational methods
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Summary:We study the existence of solutions of the Sturm–Liouville problem with a nonlinearity discontinuous with respect to the state variable. By the variational method, we prove theorems on the existence of semiregular and regular solutions, estimates for the differential operator, and properties of a “separating” set for the considered problem. These results are applied to the one-dimensional Gol’dshtik and Lavrent’ev models of separated flows of an incompressible fluid.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266115070162