论文标题
非线性非均匀奇异问题
Nonlinear nonhomogeneous singular problems
论文作者
论文摘要
我们认为由非均匀差异操作员驱动的非线性差异问题，其增长$（p-1）$接近$+\ hypty $，并且具有参数性奇异术语的竞争效果和$（p-1）$ - 超级线性扰动的竞争效果，这无法满足通常的ambrosetti-rabinowitz-rabinowitz条件。使用变异工具，再加上合适的截断和强大的比较技术，我们证明了一种“分叉型”定理，将一组正溶液描述为参数$λ$在阳性半肌上移动。我们还表明，在每$λ> 0 $中，问题都有最小的阳性解决方案$ u^*_λ$，我们演示了地图$λ\ mapsto u^*_λ$的单调性和连续性属性。
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order $(p-1)$ near $+\infty$ and with a reaction which has the competing effects of a parametric singular term and a $(p-1)$-superlinear perturbation which does not satisfy the usual Ambrosetti-Rabinowitz condition. Using variational tools, together with suitable truncation and strong comparison techniques, we prove a "bifurcation-type" theorem that describes the set of positive solutions as the parameter $λ$ moves on the positive semiaxis. We also show that for every $λ>0$, the problem has a smallest positive solution $u^*_λ$ and we demonstrate the monotonicity and continuity properties of the map $λ\mapsto u^*_λ$.
