Remarks on Existence of Large Solutions for p-Laplacian Equations with Strongly Nonlinear Terms Satisfying the Keller-Osserman Condition

Abstract

We deal with existence of large solutions of ∆

An existence result for a quasilinear system with gradientterm under the Keller--Osserman conditions

“…We mention that we can prove similar results for f 1 and f 2 being nonmonotonic, as in former papers [6] or [8] or more recently in [5], respectively [11]. Since in this case the proof is as for the monotone case, we omit it.…”

“…Finally, we note that the study of large solutions for (1) when the integral in (2) is finite has been the subject of articles by Goncalves-Jiazheng [5] and Keller [6] for the scalar case and recently by Peterson and Wood [8] in the systems case, where the authors obtained the existence of solutions for the case when (3) fails to hold. Motivated by [3], [4], [5], [11], [13], and [14], we are interested in another type of nonlinearity, f i (i = 1, 2), in order to obtain the existence of entire large/bounded positive solutions of (1).…”

“…For the systems case, basic results in the study of solutions have been obtained in the works of Bandl -Marcus [1], the present author [3], Dkhil-Zeddini [4], Goncalves-Jiazheng [5], Matero [8,9], Zhang-Liu [14], and Peterson-Wood [11] and their references. We comment below on a few further results closer to our interests in the present article.…”

“…Motivated by [3], [4], [5], [11], [13], and [14], we are interested in another type of nonlinearity, f i (i = 1, 2), in order to obtain the existence of entire large/bounded positive solutions of (1).…”

Existence and non-existence of blow-up solutions for a non-autonomous problem with indefinite and gradient terms

“…The case b = 0 is very studied. See for instance [7] with p = 2 and [30] for 1 < p < ∞ and references therein.…”