Positive solutions of nonlinear p-Laplacian equations in Rn

This paper studies the existence of positive solutions of the nonlinear p-Laplacian equation −Δpu=f(x,u) in Rn. Existence of infinitely many positive solutions is established via super–sub-solution methods. Decaying conditions on f(x,u) at |x|=∞ are imposed. Necessity of the conditions and nonexistence of positive solutions are illustrated through decay–growth estimates of solutions at infinity. Special situation and examples are checked in detail.