Remarks on Existence of Large Solutions for p-Laplacian Equations with Strongly Nonlinear Terms Satisfying the Keller-Osserman Condition
J.V. Gonçalves, Jiazheng Zhou · Advanced Nonlinear Studies · 2010
Abstract We deal with existence of large solutions of ∆ p u = a(x)f(u)+b(x)g(u) in ℝ N . It is shown that if a, b, f, g are non-negative real valued functions with a, b ∈ C(ℝ N ), f, g ∈ C([0,∞)) and f + g ≥ h where h is a continuous, non-negative, non- decreasing function satisfying the Keller-Osserman condition then the equation above admits a large solution if the equation -∆ p v = a(x) + b(x) in ℝ N has a positive upper solution decaying to zero at infinity. No monotonicity condition is required from either f or g. Our proof is based on the method of lower and upper-solutions. We extend recent results by A. V. Lair and A. Mohammed.