Abstract
In this paper, we investigate a class of second-order p(t)-Laplacian systems with local ‘superquadratic’ potential. By using the generalized mountain pass theorem, we obtain an existence result for nonconstant periodic solutions.
Highlights
1 Introduction This paper is concerned with the existence of periodic solutions for the following p(t)Laplacian system:
The p(t)-Laplacian system can be applied to describe the physical phenomena with ‘pointwise different properties’ which first arose from the nonlinear elasticity theory
Motivated by the papers [, ], we aim in this paper to study the existence of nonconstant periodic solutions of system ( ) with local ‘superquadratic’ potential and without the AR condition
Summary
This paper is concerned with the existence of periodic solutions for the following p(t)Laplacian system:. ⎨u (t) + ∇F(t, u(t)) = , t ∈ [ , T], In , Rabinowitz [ ] published his pioneer paper on the existence of periodic solutions for problem ( ) under the following Ambrosetti-Rabinowitz superquadratic condition:. Some new superquadratic conditions under which there exist periodic solutions for problem ( ) have been discovered in literature, see, for example, the references [ – ]. In [ – ], the authors studied a superlinear elliptic equation with p(x)Laplacian without the AR condition and obtained some existence results. Motivated by the papers [ , , , , ], we aim in this paper to study the existence of nonconstant periodic solutions of system ( ) with local ‘superquadratic’ potential and without the AR condition.
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