论文标题
罗宾$ p $ -laplacian的积极解决方案以及无限潜力
Positive solutions for the Robin $p$-Laplacian plus an indefinite potential
论文作者
论文摘要
我们考虑了由Robin $ p $ -laplacian驱动的非线性椭圆方程，再加上不确定的潜力。在反应中，我们具有严格的$（p-1）$ - sublrinear参数术语以及$（p-1）$ - 线性和不均匀的不均匀术语的竞争效果。我们将积极解决方案集作为参数$λ> 0 $而变化。我们证明了较大的正参数$λ$值的分叉型结果。另外，我们表明，对于所有可接受的$λ> 0 $，该问题具有最小的积极解决方案$ \ OVILLINE {u}_λ$，我们研究了地图$ cum $λ\ mapsto \ mapsto \ mapsto \ edline {u}_λ$的单调性和连续性属性。
We consider a nonlinear elliptic equation driven by the Robin $p$-Laplacian plus an indefinite potential. In the reaction we have the competing effects of a strictly $(p-1)$-sublinear parametric term and of a $(p-1)$-linear and nonuniformly nonresonant term. We study the set of positive solutions as the parameter $λ>0$ varies. We prove a bifurcation-type result for large values of the positive parameter $λ$. Also, we show that for all admissible $λ>0$, the problem has a smallest positive solution $\overline{u}_λ$ and we study the monotonicity and continuity properties of the map $λ\mapsto\overline{u}_λ$.
