Fast homoclinic solutions for a class of ordinary p-Laplacian systems

Fast homoclinic solutions for a class of ordinary p-Laplacian systems

Existence of homoclinic solutions for a class of difference systems involving p-Laplacian

*Correspondence: [email protected] College of Science, Guilin University of Technology, Guilin, Guangxi 541004, P.R. China Abstract By using the critical point theory, some existence criteria are established which guarantee that the difference p-Laplacian systems of the form (| u(n – 1)|p–2 u(n – 1)) – a(n)|u(n)|q–pu(n) +∇W(n,u(n)) = 0 have at least one or infinitely many homoclinic solutions,...

Existence of homoclinic solutions for a class of second order p-Laplacian systems with impulsive effects

This paper is concerned with the existence of homoclinic solutions for a class of second order p-Laplacian systems with impulsive effects. A new result is obtained under more relaxed conditions by using the mountain pass theorem, a weak convergence argument, and a weak version of Lieb’s lemma. MSC: 34C37; 35A15; 37J45; 47J30

Homoclinic solutions for second order discrete p-Laplacian systems

* Correspondence: hxfcsu@sina. com Department of Mathematics and Computer Science Jishou University, Jishou, Hunan 416000, P. R. China Full list of author information is available at the end of the article Abstract Some new existence theorems for homoclinic solutions are obtained for a class of second-order discrete p-Laplacian systems by critical point theory, a homoclinic orbit is obtained as...

Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian

and Applied Analysis 3 W4 W̃ n, x ∇W n, x , x − pW n, x , lim |x|→∞ W̃ n, x ∞ uniformly for n ∈ Z, 1.7 and for any fixed 0 < c1 < c2 < ∞, inf n∈Z, c1≤|x|≤c2 W̃ n, x |x| > 0. 1.8 Then problem 1.1 has at least one nontrivial homoclinic solution. Remark 1.2. The function W n, x in this paper is asymptotically p-linear at infinity. The behavior of the gradient of W n, x at infinity is like that of a f...