论文标题
各向异性奇异的诺伊曼方程，增长不平衡
Anisotropic singular Neumann equations with unbalanced growth
论文作者
论文摘要
我们考虑了由各向异性$（P，Q）$ - 拉普拉斯（Laplacian）驱动的非线性参数Neumann问题，其反应表现出奇异术语和参数超级线性扰动的综合作用。我们正在寻找积极的解决方案。使用拓扑和变分工具以及合适的截断和比较技术的组合，我们证明了分叉型结果，将一组正溶液描述为正参数$λ$的变化。我们还显示了最小正溶液的存在$u_λ^*$，并确定地图$λ\ mapstou_λ^*$的单调性和连续性属性。
We consider a nonlinear parametric Neumann problem driven by the anisotropic $(p,q)$-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive solutions. Using a combination of topological and variational tools together with suitable truncation and comparison techniques, we prove a bifurcation-type result describing the set of positive solutions as the positive parameter $λ$ varies. We also show the existence of minimal positive solutions $u_λ^*$ and determine the monotonicity and continuity properties of the map $λ\mapsto u_λ^*$.
