Abstract
We study the existence of multiple positive solutions to systems of the form \begin{equation*} \begin{cases} \qquad-{\Delta} u ={\lambda} f(v), & \text{ in }{\Omega},\\ \qquad-{\Delta} v ={\lambda} g(u), & \text{ in }{\Omega},\\ \qquad\quad~~ u=0=v, & \text{ on }{\partial}{\Omega}. \end{cases} \end{equation*} Here ${\Delta}$ is the Laplacian operator, ${\lambda}$ is a positive parameter, ${\Omega}$ is a bounded domain in ${\mathbb{R}^N}$ with smooth boundary and $f, g$ belong to a class of positive functions that have a combined sublinear effect at $\infty$. Our results also easily extend to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.
Citation
Jaffar Ali. Mythily Ramaswamy. R. Shivaji. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Differential Integral Equations 19 (6) 669 - 680, 2006. https://doi.org/10.57262/die/1356050357
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