Abstract
This paper deals with the asymptotic problems for the nonlinear differential equation (a(t)φ(x′))′+b(t)|x|γsgnx=0 involving φ-Laplacian. Necessary and sufficient conditions are given for the oscillation of solutions of this equation. Moreover, we study the existence of unbounded solutions with different asymptotic behavior, in particular, weakly increasing solutions and extremal solutions. Examples for prescribed mean curvature equation are given to illustrate our results.
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