## Existence and uniqueness of positive solutions for some quasilinear elliptic problems.(English)Zbl 0991.35035

Let $$\Omega\subset R^d$$ be a smooth bounded domain and $$1<p<d$$. Let $$\Delta_p$$ denote the $$p$$-Laplacian, that is $$\Delta_p u=\text{div} (|\nabla u|^{p-2} \nabla u)$$ and $$f:\Omega \times R\to R$$ is a Carathéodory function. The authors study the quasilinear boundary value problem $\begin{cases} -\Delta_pu= f(x,u)\quad &\text{in }\Omega\\ u=0\quad &\text{on } \partial \Omega\end{cases} \tag{*}$ and present a rather general version of the method of sub- and supersolutions for (*) with sublinear terms. Moreover the authors give several applications to sublinear problems.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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### References:

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