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<p>We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator, with a reaction exhibiting the competing effects of a parametric concave term and of a convex gradient dependent perturbation. Using the Leray-Schauder Alternative Principle, the nonlinear Hopf’s maximum principle, and the nonlinear regularity theorem, we show that for all small values of the parameter, the problem has a positive smooth solution.</p>

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Nonlinear Convective Concave-Convex Problems

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • Yunru Bai,
  • Nikolaos S. Papageorgiou,
  • Shengda Zeng

摘要

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator, with a reaction exhibiting the competing effects of a parametric concave term and of a convex gradient dependent perturbation. Using the Leray-Schauder Alternative Principle, the nonlinear Hopf’s maximum principle, and the nonlinear regularity theorem, we show that for all small values of the parameter, the problem has a positive smooth solution.