scholarly journals On Neumann hemivariational inequalities

2002 ◽  
Vol 7 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Halidias Nikolaos
Keyword(s):  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Mountain Pass ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Locally Lipschitz

We derive a nontrivial solution for a Neumann noncoercive hemivariational inequality using the critical point theory for locally Lipschitz functionals. We use the Mountain-Pass theorem due to Chang (1981).

scholarly journals Nonlinear hemivariational inequalities at resonance

1999 ◽  
Vol 60 (3) ◽  
pp. 353-364 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Point Theory ◽  
Hemivariational Inequalities ◽  
At Resonance ◽  
Locally Lipschitz

In this paper we consider nonlinear hemivariational inequalities involving the p-Laplacian at resonance. We prove the existence of a nontrivial solution. Our approach is variational based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang.

scholarly journals An existence theorem for nonlinear hemivariational inequalities at resonance

2001 ◽  
Vol 63 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Existence Theorem ◽  
Nontrivial Solution ◽  
Mountain Pass Theorem ◽  
Existence Results ◽  
Mountain Pass ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Compactness Condition ◽  
At Resonance ◽  
Recent Theorem

We consider a nonlinear hemivariational inequality with the p-Laplacian at resonance. Using an extension of the nonsmooth mountain pass theorem of Chang, which makes use of the Cerami compactness condition, we prove the existence of a nontrivial solution. Our existence results here extends a recent theorem on resonant hemivariational inequalities, by the authors in 1999.

scholarly journals Existence of Homoclinic Orbits for a Class of Asymptoticallyp-Linear Difference Systems withp-Laplacian

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Qiongfen Zhang ◽  
X. H. Tang
Keyword(s):  
Critical Point ◽  
Critical Point Theory ◽  
Mountain Pass Theorem ◽  
Homoclinic Orbits ◽  
Point Theory ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Difference System ◽  
Difference Systems ◽  
Linear Difference Systems

By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptoticallyp-linear difference system withp-LaplacianΔ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0, wherep∈(1,+∞),n∈ℤ,u∈ℝN,K,W:ℤ×ℝN→ℝare not periodic inn, and W is asymptoticallyp-linear at infinity.

scholarly journals Nontrivial solutions for a multivalued problem with strong resonance

1996 ◽  
Vol 38 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Vicenţiu D. Rădulescu
Keyword(s):  
Critical Point ◽  
Banach Spaces ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Mountain Pass ◽  
Nontrivial Solutions ◽  
Reflexive Banach Spaces ◽  
Strong Resonance ◽  
Locally Lipschitz ◽  
Critical Point Theorems

The Mountain-Pass Theorem of Ambrosetti and Rabinowitz (see [1]) and the Saddle Point Theorem of Rabinowitz (see [21]) are very important tools in the critical point theory of C1-functional. That is why it is natural to ask us what happens if the functional fails to be differentiable. The first who considered such a case were Aubin and Clarke (see [6]) and Chang (see [12]),who gave suitable variants of the Mountain-Pass Theorem for locally Lipschitz functionals which are denned on reflexive Banach spaces. For this aim they replaced the usual gradient with a generalized one, which was firstly defined by Clarke (see [13], [14]).As observed by Brezis (see [12, p. 114]), these abstract critical point theorems remain valid in non-reflexive Banach spaces.

scholarly journals Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity inR3

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ling Ding ◽  
Lin Li ◽  
Jin-Ling Zhang
Keyword(s):  
Variational Principle ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Kirchhoff Equation ◽  
Mountain Pass ◽  
Asymptotically Linear ◽  
Ekeland's Variational Principle

We study the following nonhomogeneous Kirchhoff equation:-(a+b∫R3‍|∇u|2dx)Δu+u=k(x)f(u)+h(x),  x∈R3,  u∈H1(R3),  u>0,  x∈R3, wherefis asymptotically linear with respect totat infinity. Under appropriate assumptions onk,f, andh, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.

Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance

2001 ◽  
Vol 131 (5) ◽  
pp. 1091-1111 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Variational Principle ◽  
Critical Point Theory ◽  
Multiple Solutions ◽  
Existence Theorems ◽  
Point Theory ◽  
Hemivariational Inequalities ◽  
Locally Lipschitz Functions ◽  
Strong Resonance ◽  
At Resonance ◽  
Locally Lipschitz

In this paper we consider quasilinear hemivariational inequalities at resonance. We obtain existence theorems using Landesman-Lazer-type conditions and multiplicity theorems for problems with strong resonance at infinity. Our method of proof is based on the non-smooth critical point theory for locally Lipschitz functions and on a generalized version of the Ekeland variational principle.

scholarly journals Nontrivial Solutions for Dirichlet Boundary Value Systems with the(p1,…,pn)-Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shang-Kun Wang ◽  
Wen-Wu Pan
Keyword(s):  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Nontrivial Solutions

Using critical point theory due to Bonanno (2012), we prove the existence of at least one nontrivial solution for Dirichlet boundary value systems with the(p1,…,pn)-Laplacian.

scholarly journals Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Damped Vibration Problems with Impulsive Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Qiongfen Zhang
Keyword(s):  
Critical Point Theory ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Impulsive Effects ◽  
Symmetric Mountain Pass Theorem ◽  
Existence And Multiplicity ◽  
Vibration Problems ◽  
Damped Vibration Problems

This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects. Some new results are obtained under more relaxed conditions by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory. The results obtained in this paper generalize and improve some existing works in the literature.

Sign in / Sign up

Export Citation Format

Share Document