Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: the superdiffusive case
Filippakis, Michael E.
Papageorgiou, Nikolaos S.
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Filippakis, Michael E. O'Regan, Donal; Papageorgiou, Nikolaos S. (2010). Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: the superdiffusive case. Communications on Pure and Applied Analysis 9 (6), 1507-1527
We consider a nonlinear elliptic equation of logistic type, driven by the p-Laplacian differential operator with a general superdiffusive reaction. We show that the equation exhibits a bifurcation phenomenon. Namely there is a critical value lambda(*) of the parameter lambda &gt; 0, such that, if lambda &gt; lambda(*), the equation has two nontrivial positive smooth solutions, if lambda = lambda(*), then there is one positive solution and finally if lambda is an element of (0, lambda(*)) then there is no positive solution.