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Infinitely many periodic solutions for variable exponent systems. (English) Zbl 1179.35113

Summary: We mainly consider the system \(-\Delta p(x)u= f(v)+h(u)\) in \(\mathbb R\), \(-\Delta q(x)v= g(u)+ \omega(v)\) in \(\mathbb R\), where \(1<p(x),q(x)\in C^1(\mathbb R)\) are periodic functions, and \(-\Delta p(x)u= -(|u'|^{p(x)-2}u')'\) is called \(p(x)\)-Laplacian. We give the existence of infinitely many periodic solutions under some conditions.

MSC:

35J47 Second-order elliptic systems
35J62 Quasilinear elliptic equations
35B10 Periodic solutions to PDEs
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References:

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