Properties of the solutions set for a class of nonlinear evolution inclusions with nonlocal conditions

Jingrui Zhang; Yi Cheng; Changqin Yuan; Fuzhong Cong

doi:10.1186/1687-2770-2013-15

Properties of the solutions set for a class of nonlinear evolution inclusions with nonlocal conditions

Jingrui Zhang^*
, Yi Cheng
, Changqin Yuan
, Fuzhong Cong

^*此作品的通讯作者

空天科学与技术学院

Aviation University of Air Force
Jilin University

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

In this paper, we consider the nonlocal problems for nonlinear first-order evolution inclusions in an evolution triple of spaces. Using techniques from multivalued analysis and fixed point theorems, we prove existence theorems of solutions for the cases of a convex and of a nonconvex valued perturbation term with nonlocal conditions. Also, we prove the existence of extremal solutions and a strong relaxation theorem. Some examples are presented to illustrate the results.

源语言	英语
期刊论文编号	15
期刊	Boundary Value Problems
卷	2013
DOI	https://doi.org/10.1186/1687-2770-2013-15
出版状态	已出版 - 2013

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10.1186/1687-2770-2013-15

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title = "Properties of the solutions set for a class of nonlinear evolution inclusions with nonlocal conditions",

abstract = "In this paper, we consider the nonlocal problems for nonlinear first-order evolution inclusions in an evolution triple of spaces. Using techniques from multivalued analysis and fixed point theorems, we prove existence theorems of solutions for the cases of a convex and of a nonconvex valued perturbation term with nonlocal conditions. Also, we prove the existence of extremal solutions and a strong relaxation theorem. Some examples are presented to illustrate the results.",

keywords = "Evolution inclusions, Extremal solutions, Leray-Schauder alternative theorem, Nonlocal conditions",

author = "Jingrui Zhang and Yi Cheng and Changqin Yuan and Fuzhong Cong",

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doi = "10.1186/1687-2770-2013-15",

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T1 - Properties of the solutions set for a class of nonlinear evolution inclusions with nonlocal conditions

AU - Zhang, Jingrui

AU - Cheng, Yi

AU - Yuan, Changqin

AU - Cong, Fuzhong

PY - 2013

Y1 - 2013

N2 - In this paper, we consider the nonlocal problems for nonlinear first-order evolution inclusions in an evolution triple of spaces. Using techniques from multivalued analysis and fixed point theorems, we prove existence theorems of solutions for the cases of a convex and of a nonconvex valued perturbation term with nonlocal conditions. Also, we prove the existence of extremal solutions and a strong relaxation theorem. Some examples are presented to illustrate the results.

AB - In this paper, we consider the nonlocal problems for nonlinear first-order evolution inclusions in an evolution triple of spaces. Using techniques from multivalued analysis and fixed point theorems, we prove existence theorems of solutions for the cases of a convex and of a nonconvex valued perturbation term with nonlocal conditions. Also, we prove the existence of extremal solutions and a strong relaxation theorem. Some examples are presented to illustrate the results.

KW - Evolution inclusions

KW - Extremal solutions

KW - Leray-Schauder alternative theorem

KW - Nonlocal conditions

UR - https://www.scopus.com/pages/publications/84888018616

U2 - 10.1186/1687-2770-2013-15

DO - 10.1186/1687-2770-2013-15

M3 - Article

AN - SCOPUS:84888018616

SN - 1687-2762

VL - 2013

JO - Boundary Value Problems

JF - Boundary Value Problems

M1 - 15

ER -

Properties of the solutions set for a class of nonlinear evolution inclusions with nonlocal conditions

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