Positive solutions for a system of second-order quasilinear boundary value problems. (June 2020)

• Record Type: Journal Article
• Authors: Yang, Zhilin; Wang, Xiaomei; Li, Hongyu
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 34B15 -- 34B18 -- 47H07 -- 47H11 -- 26D10; Quasilinear boundary value problem -- Positive solution -- A priori estimate -- Fixed point index -- Jensen's inequality -- Homogeneous operator; 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.2020.111749
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the existence and multiplicity of positive solutions for the system of second-order quasilinear boundary value problems − ( ( u ′ ) p − 1 ) ′ = f ( t, u, v ), − ( ( v ′ ) q − 1 ) ′ = g ( t, u, v ), u ( 0 ) = u ′ ( 1 ) = 0, v ( 0 ) = v ′ ( 1 ) = 0, where p, q > 1 and f, g ∈ C ( [ 0, 1 ] × R + 2, R + ) ( R + ≔ [ 0, ∞ ) ) . Based on a priori estimates achieved by utilizing Jensen's inequality for nonnegative concave functions and homogeneous operators, we use fixed point index theory to establish the main results.