scholarly journals Existence and subharmonicity of solutions for nonsmooth $ p $-Laplacian systems

2021 ◽  
Vol 6 (10) ◽  
pp. 10947-10963
Author(s):  
Yan Ning ◽  
◽  
Daowei Lu ◽  
Anmin Mao ◽  
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Potential Function ◽  
Critical Point Theory ◽  
Point Theory ◽  
Periodic Systems ◽  
Nonsmooth Critical Point Theory ◽  
Nonsmooth Critical Point ◽  
Locally Lipschitz

<abstract><p>In this paper we study nonlinear periodic systems driven by the vectorial $ p $-Laplacian with a nonsmooth locally Lipschitz potential function. Using variational methods based on nonsmooth critical point theory, some existence of periodic and subharmonic results are obtained, which improve and extend related works.</p></abstract>

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.

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.

scholarly journals Nonsmooth critical point theory and nonlinear elliptic equations at resonance

2000 ◽  
Vol 69 (2) ◽  
pp. 245-271 ◽  
Author(s):  
Nikolaos C. Kourogenis ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Critical Point ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Nonlinear Elliptic Equations ◽  
Point Theory ◽  
Energy Functional ◽  
Existence Theory ◽  
Nonsmooth Critical Point Theory ◽  
Nonsmooth Critical Point ◽  
The Right

AbstractIn this paper we complete two tasks. First we extend the nonsmooth critical point theory of Chang to the case where the energy functional satisfies only the weaker nonsmooth Cerami condition and we also relax the boundary conditions. Then we study semilinear and quasilinear equations (involving the p-Laplacian). Using a variational approach we establish the existence of one and of multiple solutions. In simple existence theorems, we allow the right hand side to be discontinuous. In that case in order to have an existence theory, we pass to a multivalued approximation of the original problem by, roughly speaking, filling in the gaps at the discontinuity points.

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 Nonlinear Periodic Systems with thep-Laplacian: Existence and Multiplicity Results

2007 ◽  
Vol 2007 ◽  
pp. 1-23
Author(s):  
Francesca Papalini
Keyword(s):  
Existence Theorems ◽  
Point Theory ◽  
Energy Functional ◽  
Periodic Systems ◽  
Multiplicity Result ◽  
Nonsmooth Critical Point Theory ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Nonsmooth Critical Point ◽  
Locally Lipschitz

We study second-order nonlinear periodic systems driven by the vectorp-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical point theory, we prove existence theorems and a multiplicity result. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (unbounded from both above and below).

Subdifferential Calculus and Nonsmooth Critical Point Theory

2000 ◽  
Vol 10 (4) ◽  
pp. 1020-1048 ◽  
Author(s):  
Ines Campa ◽  
Marco Degiovanni
Keyword(s):  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Nonsmooth Critical Point Theory ◽  
Subdifferential Calculus ◽  
Nonsmooth Critical Point

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.

Sign in / Sign up

Export Citation Format

Share Document