We consider a nonlinear Robin problem associated to the p-Laplacian plus an indefinite potential. In the reaction we have the competing effects of two nonlinear terms. One is parametric and strictly \((p-1)\)-sublinear. The other is \((p-1)\)-linear. We prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter \(\lambda >0\). We also show that for every admissible parameter the problem has a smallest positive solution \({\bar{u}}_{\lambda }\) and we study monotonicity and continuity properties of the map \(\lambda \rightarrow {\bar{u}}_{\lambda }\).

中文翻译：

---

具有不确定势和竞争非线性的非线性Robin问题的正解

我们考虑与p -Laplacian关联的非线性Robin问题以及一个不确定的电位。在反应中，我们具有两个非线性项的竞争效应。一个是参数化的，严格上是\（（p-1）\）-次线性。另一个是\（（p-1）\）- linear。我们证明了一个分叉型定理，描述了正解集对参数\（\ lambda> 0 \）的依赖性。我们还表明，对于每个允许的参数，问题都有一个最小的正解\（{\ bar {u}} _ {\ lambda} \），并且我们研究地图\（\ lambda \ rightarrow {\ bar {u}} _ {\ lambda} \）。