2 research outputs found
Positive Solutions for a Derivative Dependent p-Laplacian Equation with Riemann-Stieltjes Integral Boundary Conditions
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
We study positive solutions to nonlinear elliptic systems of the form: \begin{eqnarray*} -\Delta u =\lambda f(v) \mbox{ in }\Omega\\-\Delta v =\lambda g(u) \mbox{ in }\Omega\\\quad~~ u=0=v \mbox{ on }\partial\Omega \end{eqnarray*} where is the Laplacian of , is a positive parameter and is a bounded domain in with smooth boundary . In particular, we will analyze the combined effects of the nonlinearities on the existence and multiplicity of positive solutions. We also study systems with multiparameters and stronger coupling. We extend our results to --Laplacian systems and to systems. We mainly use sub- and super-solutions to prove our results