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Bounded positive entire solutions of singular quasilinear elliptic equations

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
235
Issue
2
Identifiers
DOI: 10.1016/j.jde.2007.01.007
Keywords
  • Singular Equation
  • Quasilinear Elliptic Equation
  • Positive Entire Solutions
  • Bounded Solution
  • Supersolution
  • Subsolution

Abstract

Abstract Suppose that β ⩾ 0 is a constant and that f : R N × R + × R N → R is a continuous function with R + : = ( 0 , ∞ ) . This paper investigates N-dimensional singular, quasilinear elliptic equations of the form Δ u + f ( x , u , ∇ u ) u − β = 0 , x ∈ R N ( N ⩾ 3 ) and gives some sufficient conditions for the equations to have (i) a decaying positive entire solution or (ii) infinitely many positive entire solutions each of which is bounded with a positive lower-bound.

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