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Positive solutions to a class of elliptic boundary value problems. (English) Zbl 0915.35043
Summary: We prove the existence of positive solutions to the boundary value problems $\Delta u+\lambda a(x)f(u)= 0\quad\text{in }\Omega,\quad u= 0\quad\text{on }\partial\Omega,$ where $$\Omega$$ is a bounded domain in $$\mathbb{R}^N$$, $$a:\Omega\to \mathbb{R}$$ may change sign, $$f(0)>0$$, and $$\lambda> 0$$ is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem. $$\copyright$$ Academic Press.

MSC:
 35J65 Nonlinear boundary value problems for linear elliptic equations
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References:
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