Remarks on the Existence Results for Second-Order Differential Inclusions with Nonlocal Conditions

2009 ◽  
Vol 15 (1) ◽  
pp. 27-43 ◽  
Author(s):  
Mohamed Bahaj
Keyword(s):  
Differential Inclusions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Second Order

scholarly journals Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hernán R. Henríquez ◽  
Marcos Rabelo ◽  
Luciana Vale
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Cauchy Problems ◽  
Impulsive Conditions

In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.

PERIODIC SOLUTIONS OF SECOND-ORDER DIFFERENTIAL INCLUSIONS SYSTEMS WITH (q, p)-LAPLACIAN

2011 ◽  
Vol 09 (02) ◽  
pp. 201-223 ◽  
Author(s):  
DANIEL PAŞCA
Keyword(s):  
Periodic Solutions ◽  
Differential Inclusions ◽  
Existence Results ◽  
Second Order

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with (q, p)-Laplacian.

Impulsive differential inclusions via variational method

2017 ◽  
Vol 24 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Mouffak Benchohra ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Differential Inclusion ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Impulsive Differential Inclusions

AbstractIn this paper, we establish several results about the existence of second-order impulsive differential inclusion with periodic conditions. By using critical point theory, several new existence results are obtained. We also provide an example in order to illustrate the main abstract results of this paper.

scholarly journals Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

scholarly journals Periodic Solutions of Second-Order Differential Inclusions Systems with -Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Liang Zhang ◽  
Peng Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Nonsmooth Critical Point Theory ◽  
Nonsmooth Critical Point ◽  
Existence Of Periodic Solutions

The existence of periodic solutions for nonautonomous second-order differential inclusion systems with -Laplacian is considered. We get some existence results of periodic solutions for system, a.e. , , by using nonsmooth critical point theory. Our results generalize and improve some theorems in the literature.

scholarly journals Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lizhen Chen ◽  
Gang Li
Keyword(s):  
Differential Inclusions ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Lipschitz Continuous ◽  
Nonlocal Initial Conditions ◽  
Nonlinear Alternative ◽  
Noncompactness Measure ◽  
Fractional Differential

In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models.

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