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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.

35J65 Nonlinear boundary value problems for linear elliptic equations
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