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We consider a second order periodic system driven by a nonhomogeneous differential operator with variable growth and a reaction that involves two competing nonlinearities. A parametric “concave (sublinear)” term and a “convex (superlinear)” term. Using variational tools (critical point theory) and critical groups, we show that the system has at least two distinct nontrivial solutions.

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Nonlinear Periodic Systems with Variable Exponents

  • 章节

  • 发表日期：

    2026年

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  • Zhenhai Liu,
  • Nikolaos S. Papageorgiou

摘要

We consider a second order periodic system driven by a nonhomogeneous differential operator with variable growth and a reaction that involves two competing nonlinearities. A parametric “concave (sublinear)” term and a “convex (superlinear)” term. Using variational tools (critical point theory) and critical groups, we show that the system has at least two distinct nontrivial solutions.