Abstract
We mainly consider the system in , in , where are periodic functions, and is called -Laplacian. We give the existence of infinitely many periodic solutions under some conditions.
Highlights
The study of differential equations and variational problems with variable exponent growth conditions has been a new and interesting topic
We mainly consider the existence of infinitely many periodic solutions for the system
If p x ≡ p a constant and q x ≡ q a constant, P is the well-known constant exponent system. u, v is called a solution of P, if u, v ∈ C1 R, |u |p x −2u and |v |p x −2v are absolute continuous and satisfy P almost every where
Summary
The study of differential equations and variational problems with variable exponent growth conditions has been a new and interesting topic. Many results have been obtained on this kind of problems, for example 1–18. We mainly consider the existence of infinitely many periodic solutions for the system. The operator −Δp x u − |u |p x −2u is called onedimensional p x -Laplacian. If p x ≡ p a constant and q x ≡ q a constant , P is the well-known constant exponent system. U, v is called a solution of P , if u, v ∈ C1 R , |u |p x −2u and |v |p x −2v are absolute continuous and satisfy P almost every where If p x ≡ p a constant and q x ≡ q a constant , P is the well-known constant exponent system. u, v is called a solution of P , if u, v ∈ C1 R , |u |p x −2u and |v |p x −2v are absolute continuous and satisfy P almost every where
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