Karakostas fixed point theorem and semilinear neutral differential equations with impulses and nonlocal conditions

• Autorzy: Leiva Hugo , Riera Lenin , Lalvay Sebastián

Identyfikatory

DOI

10.7862/rf.2022.5

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the existence and uniqueness of solutions for a semilinear neutral differential equation with impulses and nonlocal conditions. First, we assume that the nonlinear terms are locally Lipschitz, and to achieve the existence of solutions, Karakostas Fixed Point Theorem is applied. After that, under some additional conditions, the uniqueness is proved as well. Next, assuming some bound on the non-linear terms the global existence is proved by applying a generalization of Gronwall inequality for impulsive differential equations. Then, we suppose stronger hypotheses on the nonlinear functions, such as globally Lipschitz conditions, that allow us to appy Banach Fixed Point Theorem to prove the existence and uniqueness of solutions. Finally, we present an example as an application of our method.

Słowa kluczowe

EN

semilinear neutral differential equations; impulses; delay; nonlocal conditions; Karakostas fixed point theorem

PL

równanie różniczkowe neutralne; impulsy; opóźnienie; warunki nielokalne; twierdzenie Karakostasa o punkcie stałym

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2022
• Tom: Vol. 45
• Strony: 107--128
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Leiva Hugo

• Department of Mathematics, School of Mathematical and Computational Sciences, Yachay Tech, San Miguel de Urcuqui, Imbabura, Ecuador

• https://orcid.org/0000-0002-3521-6253

autor

Riera Lenin

• Department of Mathematics, School of Mathematical and Computational Sciences, Yachay Tech, San Miguel de Urcuqui, Imbabura, Ecuador

• https://orcid.org/0000-0002-4803-4918

autor

Lalvay Sebastián

• Department of Mathematics, School of Mathematical and Computational Sciences, Yachay Tech, San Miguel de Urcuqui, Imbabura, Ecuador

• https://orcid.org/0000-0002-0480-0828

Bibliografia

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