Solutions with a prescribed interval of positivity for differential systems with nonlocal conditions

Abstract

Based on fixed point index, the paper develops a theory of existence, localization and multiplicity of solutions to first-order differential systems subject to linear nonlocal conditions.

The main features concern the role of the support of the nonlocal condition and the positivity of solutions which is only required on a prescribed subinterval.

Several examples of problems admitting at least one, two, or sequences of such solutions are included, and numerical solutions are obtained using the Mathematica shooting program with starting initial conditions suggested by the theoretical localization results.

Authors

Veronica Ilea
Department of Mathematics, Babeş-Bolyai University,  Cluj-Napoca, Romania
Adela Novac
Department of Mathematics, Technical University of Cluj-Napoca,  Romania
Diana Otrocol
Department of Mathematics, Technical University of Cluj-Napoca,  Romania
Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy)
Radu Precup
Department of Mathematics, Babeş-Bolyai University, Romania

Keywords

Differential system; Nonlocal condition; Positive solution; Multiple solutions; Fixed point index

References

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Paper coordinates

V. Ilea, A. Novac, D. Otrocol, R. Precup, Solutions with a prescribed interval of positivity for differential systems with nonlocal conditions, Appl. Math. Comput., 375 (2020), doi: 10.1016/j.amc.2020.125092

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Elsevier

Publisher Name

Applied Mathematics and Computation

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