Periodic solutions for some nonautonomous p(t)-Laplacian Hamiltonian systems

Zhang, Liang; Tang, Xianhua

doi:10.1007/s10492-013-0002-x

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…In [7][8][9][10][11][12][13][14][15], the authors studied the existence of periodic solutions, subharmonic solutions and homoclinic orbits for the p(t)-Laplacian systems ⎧ ⎨ ⎩ d dt (|u(t)| p(t)-2u (t)) + ∇V (t, u(t)) = 0, a.e. t ∈ [0, T] u(0)u(T) =u(0) -u(T) = 0, (1.2) where p(t) ∈ C([0, T], R + ), the operator d dt (|u(t)| p(t)-2u (t)) is said to be p(t)-Laplacian.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Periodic solutions for nonlocal $p(t)$-Laplacian systems

Shengui

2019

Bound Value Probl

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The purpose of this paper is to investigate the existence of periodic solutions for a class of nonlocal p(t)-Laplacian systems. When the nonlinear term is p +-superlinear at infinity, some new solvability conditions of nontrivial periodic solutions are obtained by using a version of the local linking theorem. A major point is that we ensure compactness without the well-known Ambrosetti-Rabinowitz type superlinearity condition. In addition, by applying the saddle point theorem, we established the existence of at least one periodic solution for such problems with a p-subquadratic potential.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Then all the conditions of Theorem 1.1 hold, and V is not covered by results in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%