Existence and multiplicity results for generalized logistic equations. (October 2016)

• Record Type: Journal Article
• Authors: Huy, Nguyen Bich; Quan, Bui The; Khanh, Nguyen Huu
• Is Part Of: Nonlinear analysis. Volume 144(2016)
• Page Start: 77
• Page End: 92
• Publication Date: 2016-10
• Subjects: 35J60 -- 47H07 -- 47H10; Logistic equation -- Dependence on the gradient -- Fixed point index -- Leggett–Williams theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.06.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider elliptic Dirichlet problem − Δ p u = λ f ( x, u, ∇ u ) − g ( x, u ) in Ω, u = 0 on ∂ Ω . Assume that the nonlinearity f satisfies certain growth condition. Using the fixed point index, the Leggett–Williams theorem on fixed point and the arguments on monotone minorant, we prove the existence and multiplicity results for the equation. This extends some known results.