Existence results of solutions for a neutral evolution equation with nonlocal conditions on infinite interval

Nan Cao; Xianlong Fu

doi:10.1016/j.jmaa.2022.126008

Existence results of solutions for a neutral evolution equation with nonlocal conditions on infinite interval

Nan Cao
, Xianlong Fu^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

This paper focuses on the study of existence and regularity of solutions for a semi-linear neutral differential equation defined on [0,+∞) with state dependent nonlocal condition. The existence and regularity of solutions on infinite interval of the considered equation, including the existence of Hölder continuous solutions, are respectively investigated by the theory of fractional power operators and fixed point theorems under some conditions for the nonlinear functions. An example is also provided to illustrate the applications of the obtained results.

Original language	English
Article number	126008
Journal	Journal of Mathematical Analysis and Applications
Volume	510
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126008
State	Published - 1 Jun 2022

Keywords

Analytic semigroup
Evolution equation
Fractional power
Nonlocal condition
Regularity

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10.1016/j.jmaa.2022.126008

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title = "Existence results of solutions for a neutral evolution equation with nonlocal conditions on infinite interval",

abstract = "This paper focuses on the study of existence and regularity of solutions for a semi-linear neutral differential equation defined on [0,+∞) with state dependent nonlocal condition. The existence and regularity of solutions on infinite interval of the considered equation, including the existence of H{\"o}lder continuous solutions, are respectively investigated by the theory of fractional power operators and fixed point theorems under some conditions for the nonlinear functions. An example is also provided to illustrate the applications of the obtained results.",

keywords = "Analytic semigroup, Evolution equation, Fractional power, Nonlocal condition, Regularity",

author = "Nan Cao and Xianlong Fu",

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AU - Cao, Nan

AU - Fu, Xianlong

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N2 - This paper focuses on the study of existence and regularity of solutions for a semi-linear neutral differential equation defined on [0,+∞) with state dependent nonlocal condition. The existence and regularity of solutions on infinite interval of the considered equation, including the existence of Hölder continuous solutions, are respectively investigated by the theory of fractional power operators and fixed point theorems under some conditions for the nonlinear functions. An example is also provided to illustrate the applications of the obtained results.

AB - This paper focuses on the study of existence and regularity of solutions for a semi-linear neutral differential equation defined on [0,+∞) with state dependent nonlocal condition. The existence and regularity of solutions on infinite interval of the considered equation, including the existence of Hölder continuous solutions, are respectively investigated by the theory of fractional power operators and fixed point theorems under some conditions for the nonlinear functions. An example is also provided to illustrate the applications of the obtained results.

KW - Analytic semigroup

KW - Evolution equation

KW - Fractional power

KW - Nonlocal condition

KW - Regularity

UR - https://www.scopus.com/pages/publications/85123195249

U2 - 10.1016/j.jmaa.2022.126008

DO - 10.1016/j.jmaa.2022.126008

M3 - 文章

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SN - 0022-247X

VL - 510

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 126008

ER -

Existence results of solutions for a neutral evolution equation with nonlocal conditions on infinite interval

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Keywords

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