Nonlocal nonlinear differential equations with a measure of noncompactness in Banach spaces

Xue, Xingmei

doi:10.1016/j.na.2008.03.046

Cited by 61 publications

(46 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Garcia-Falset [18] studied the existence and asymptotic bahavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces. Xue [34] studied the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions under non-compactness conditions. Cui and Yan [13] discussed the existence of mild solutions for a class of fractional neutral stochastic integro-differential equations with infinite delay in Hilbert spaces.…”

Section: α T U(t) = Au(t) + F (T U(t)) T ∈ (0 B] U(0) = G(u)mentioning

confidence: 99%

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

Peng

Gao

2012

fcaa

View full text Add to dashboard Cite

show abstract

Section: α T U(t) = Au(t) + F (T U(t)) T ∈ (0 B] U(0) = G(u)mentioning

confidence: 99%

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

Peng

Gao

2012

fcaa

View full text Add to dashboard Cite

show abstract

“…In recent decades, existence of mild solutions of nonlocal Cauchy problems has been investigated extensively by many researchers (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references cited therein). The study of abstract nonlocal semilinear initial value problems was initiated by Byszewski and Lakshmikantham [11] and Byszewski [12].…”

Section: Introductionmentioning

confidence: 99%

Existence of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions

Qin

et al. 2017

Journal of Function Spaces

View full text Add to dashboard Cite

This paper is concerned with the existence results of nonlocal problems for a class of fractional impulsive integrodifferential equations in Banach spaces. We define a piecewise continuous control function to obtain the results on controllability of the corresponding fractional impulsive integrodifferential control systems. The results are obtained by means of fixed point methods. An example to illustrate the applications of our main results is given.

show abstract

“…Then it has been studied extensively under various conditions, see [3,4,7,8,13,14,21]. Byszewski and Lakshmikantham [9] obtained the existence and uniqueness of mild solutions in the case that Lipschitz-type conditions are satisfied.…”

Section: Introductionmentioning

confidence: 99%

On the evolution differential inclusions under a noncompact evolution system

Min¹,

Ji²,

Wen³

2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

We study the existence of mild solutions to differential inclusions with nonlocal conditions. The first result is established when evolution system is equicontinuous and multifunction is upper semi-continuous. Then another result is obtained when evolution system is not equicontinuous and not compact. The measure of noncompactness and the fixed point theorem for multivalued mappings play key roles in the proof. An example is provided to illustrate our results.

show abstract

Nonlocal nonlinear differential equations with a measure of noncompactness in Banach spaces

Cited by 61 publications

References 21 publications

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

Existence of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions

On the evolution differential inclusions under a noncompact evolution system

Contact Info

Product

Resources

About