We prove that the semilinear elliptic equation , in , , on has a positive solution when the nonlinearity belongs to a class which satisfies at infinity and behaves like near the origin, where if and if . In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of .
"On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers." Abstr. Appl. Anal. 2008 1 - 6, 2008. https://doi.org/10.1155/2008/578417