Existence and Asymptotic Properties of the Solution of a Nonlinear Boundary-Value Problem on the Real Axis

We consider a nonlinear system of ordinary differential equations defined on the entire real axis with Dirichlet-type boundary conditions at˙±∞. It is assumed that the linear part of the system has the property of nonuniform strong exponential dichotomy. To prove the existence theorem, we apply a Sc...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-05, Vol.263 (2), p.248-257
Main Authors: Parasyuk, I. O., Protsak, L. V.
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary conditions
Boundary value problems
Differential equations
Dirichlet problem
Existence theorems
Fixed points (mathematics)
Mathematics
Mathematics and Statistics
Nonlinear systems
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Summary:We consider a nonlinear system of ordinary differential equations defined on the entire real axis with Dirichlet-type boundary conditions at˙±∞. It is assumed that the linear part of the system has the property of nonuniform strong exponential dichotomy. To prove the existence theorem, we apply a Schauder–Tikhonov-type fixed-point principle. In addition, we also establish conditions under which the obtained solution has the same asymptotic properties as the solution of the inhomogeneous linearized system.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05923-8