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 Periodic Solutions for Semilinear Fourth-Order Differential Inclusions via Nonsmooth Critical Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bian-Xia Yang ◽  
Hong-Rui Sun
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Nonsmooth Critical Point Theory ◽  
Critical Point Theorem ◽  
Related Literature ◽  
Nonsmooth Critical Point

Three periodic solutions with prescribed wavelength for a class of semilinear fourth-order differential inclusions are obtained by using a nonsmooth version critical point theorem. Some results of previous related literature are extended.

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 Three Solutions for Fourth-Order Impulsive Differential Inclusions via Nonsmooth Critical Point Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Dongdong Gao ◽  
Jianli Li
Keyword(s):  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Three Solutions ◽  
Nonsmooth Critical Point Theory ◽  
Critical Point Theorem ◽  
Impulsive Differential Inclusions ◽  
Nonsmooth Critical Point

An existence of at least three solutions for a fourth-order impulsive differential inclusion will be obtained by applying a nonsmooth version of a three-critical-point theorem. Our results generalize and improve some known results.

scholarly journals Periodic Solutions for Second-Order Ordinary Differential Equations with Linear Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaohong Hu ◽  
Dabin Wang ◽  
Changyou Wang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Minimax Methods ◽  
Existence Of Periodic Solutions

By using minimax methods in critical point theory, we obtain the existence of periodic solutions for second-order ordinary differential equations with linear nonlinearity.

Existence of Periodic Solutions for a Class of Second-Order Nonlinear Difference Systems

2011 ◽  
Vol 148-149 ◽  
pp. 1164-1169
Author(s):  
Wei Ming Tan ◽  
Fang Su
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sufficient Condition ◽  
Order Difference ◽  
Difference Systems ◽  
Existence Of Periodic Solutions

In this paper, by using critical point theory, a sufficient condition is obtained on the existence of periodic solutions for a class of nonlinear second-order difference systems.

scholarly journals Existence of Periodic Solutions for a Class of Asymptoticallyp-Linear Discrete Systems Involvingp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Kai Chen ◽  
Qiongfen Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Mountain Pass Theorem ◽  
Discrete Systems ◽  
Point Theory ◽  
Existence Results ◽  
Existence Of Periodic Solutions ◽  
Linear Discrete Systems

By applying Mountain Pass Theorem in critical point theory, two existence results are obtained for the following asymptoticallyp-linearp-Laplacian discrete systemΔ(|Δu(t−1)|p−2Δu(t−1))+∇[−K(t,u(t))+W(t,u(t))]=0. The results obtained generalize some known works.

scholarly journals Perturbation results involving the 1-Laplace operator

2019 ◽  
Vol 12 (3) ◽  
pp. 277-302 ◽  
Author(s):  
Samuel Littig ◽  
Friedemann Schuricht
Keyword(s):  
Critical Point ◽  
Laplace Operator ◽  
Critical Point Theory ◽  
Eigenvalue Problems ◽  
Point Theory ◽  
Nonsmooth Critical Point Theory ◽  
Unperturbed Problem ◽  
Nonsmooth Critical Point

AbstractWe consider perturbed eigenvalue problems of the 1-Laplace operator and verify the existence of a sequence of solutions. It is shown that the eigenvalues of the perturbed problem converge to the corresponding eigenvalue of the unperturbed problem as the perturbation becomes small. The results rely on nonsmooth critical point theory based on the weak slope.

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