Homoclinic orbits for a class ofp-Laplacian systems with periodic assumption

Homoclinic orbits for a class of p-Laplacian systems with periodic assumption

In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the p-Laplacian system d(|u̇(t)|p−2u̇(t))/dt + ∇V (t, u(t)) = f(t), where p > 1, V (t, x) = −K(t, x) + W (t, x).

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...

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

INFINITELY MANY HOMOCLINIC ORBITS OF SECOND-ORDER p-LAPLACIAN SYSTEMS

In this paper, we give several new sufficient conditions for the existence of infinitely many homoclinic orbits of the second-order ordinary p-Laplacian system d dt (|u̇(t)|p−2u̇(t)) − a(t)|u(t)|p−2u(t) +∇W (t, u(t)) = 0, where p > 1, t ∈ R, u ∈ R , a ∈ C(R,R) and W ∈ C(R × R ,R) are no periodic in t, which greatly improve the known results due to Rabinowitz and Willem.

Degenerate periodic orbits and homoclinic torus bifurcation.

A one-parameter family of periodic orbits with frequency omega and energy E of an autonomous Hamiltonian system is degenerate when E'(omega) = 0. In this paper, new features of the nonlinear bifurcation near this degeneracy are identified. A new normal form is found where the coefficient of the nonlinear term is determined by the curvature of the energy-frequency map. An important property of t...