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 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.

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