• Explosive solutions of elliptic equations with absorption and nonlinear gradient term

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/112/03/0441-0451

• # Keywords

Explosive solution; semilinear elliptic problem; entire solution; maximum principle

• # Abstract

Letf be a non-decreasing C1-function such that$$f &gt; 0 on (0,\infty ), f(0) = 0, \int_1^\infty {1/\sqrt {F(t)} dt&lt; \infty }$$ andF(t)/f2a(t)→ 0 ast → ∞, whereF(t)=∫0tf(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|a=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded.

• # Author Affiliations

1. Department of Mathematics, University of Craiova, Craiova - 1100, Romania

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019