Influence of singular weights on the asymptotic behavior of positive solutions for classes of quasilinear equations

Abstract

Main objective of this paper is to study positive decaying solutions for a class of quasilinear problems with weights. We consider one dimensional problems on an interval which may be finite or infinite. In particular, when the interval is infinite, unlike the known cases in the history where constant weights force the solution not to decay, we discuss singular weights in the diffusion and reaction terms which produce positive solutions that decay to zero at infinity. We also discuss singular weights that lead to positive solutions not satisfying Hopf's boundary lemma. Further, we apply our results to radially symmetric solutions to classes of problems in higher dimensions, say in an annular domain or in the exterior region of a ball. Finally, we provide examples to illustrate our results.

Keywords

• quasilinear problems
• singular weights
• asymptotic behavior
• decaying positive solutions