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

^*Corresponding author for this work

School of Aerospace Engineering

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

3 Citations (Scopus)

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.

Original language	English
Article number	15
Journal	Boundary Value Problems
Volume	2013
DOIs	https://doi.org/10.1186/1687-2770-2013-15
Publication status	Published - 2013

Keywords

Evolution inclusions
Extremal solutions
Leray-Schauder alternative theorem
Nonlocal conditions

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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.",

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

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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

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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

Abstract

Keywords

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