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      Permanent link:
      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$$f > 0 on (0,\infty ), f(0) = 0, \int_1^\infty {1/\sqrt {F(t)} dt< \infty } $$ 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

       

      Marius Ghergu1 Constantin Niculescu1 Vicenţiu Rădulescu1

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

    • Dates

       
      Published
      August 2002
      Manuscript received
      22 February 2002
      Manuscript revised
      23 May 2002

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