The semi-linear

SEMILINEAR PROBLEMS WITH BOUNDED NONLINEAR TERM MARTIN SCHECHTER Received 17 August 2004 We solve boundary value problems for elliptic semilinear equations in which no asymptotic behavior is prescribed for the nonlinear term. 1. Introduction Many authors (beginning with Landesman and Lazer [1]) have studied resonance problems for semilinear elliptic partial differential equations of the form −∆u − λ u = f (x,u) in Ω, u = 0 on ∂Ω, (1.1) where Ω is a smooth bounded domain in Rn , λ is an eigenvalue of the linear problem −∆u = λu in Ω, u = 0 on ∂Ω, (1.

8p sting12 10-03-2012 35 3   Download

MONOTONE ITERATIVE TECHNIQUE FOR SEMILINEAR ELLIPTIC SYSTEMS A. S. VATSALA AND JIE YANG Received 27 September 2004 and in revised form 23 January 2005 We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower solutions, we develop monotone iterative technique.

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