Abstract
We are concerned with the following semilinear elliptic equation $\Delta u=\lambda f\left( x,u\right) $ in $D,$ subject to some Dirichlet conditions, where $\lambda \geq 0$ is a parameter and $D$ is a smooth domain in $\mathbb{R}^{n}\left( n\geq 3\right) $. Under some appropriate assumptions on the nonnegative nonlinearity term $f\left( x,u\right) ,$ we show the existence of a positive bounded solution for the above semilinear elliptic equation. Our approach is based on Schauder's fixed point Theorem.
Citation
Imed Bachar. Habib Mâagli. "Positive bounded solutions for semilinear elliptic equations in smooth domains." Bull. Belg. Math. Soc. Simon Stevin 20 (4) 707 - 714, october 2013. https://doi.org/10.36045/bbms/1382448190
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