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

We deal with existence of large solutions of ∆ u = a(x)f(u)+b(x)g(u) in ℝ . It is shown that if a, b, f, g are non-negative real valued functions with a, b ∈ C(ℝ ), f, g ∈ C([0,∞)) and f + g ≥ h where h is a continuous, non-negative, non- decreasing function satisfying the Keller-Osserman condition...

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Bibliographic Details
Published in:Advanced nonlinear studies 2010-11, Vol.10 (4), p.757-769
Main Authors: Goncalves, J. V. A., Zhou, Jiazheng
Format: Article
Language:English
Subjects:
Keller-Osserman condition
large solutions
quasilinear equations
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Summary:We deal with existence of large solutions of ∆ u = a(x)f(u)+b(x)g(u) in ℝ . It is shown that if a, b, f, g are non-negative real valued functions with a, b ∈ C(ℝ ), 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 -∆ v = a(x) + b(x) in ℝ 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.
ISSN:1536-1365
2169-0375
DOI:10.1515/ans-2010-0402