Zhang, Kemei; Sun, Jingxian Multiple solutions for superlinear operator equations in Banach spaces and applications. (Chinese. English summary) Zbl 1117.47304 Acta Math. Sin. 48, No. 1, 99-108 (2005). Summary: Existence of multiple solutions for a kind of superlinear operator equations is discussed via two coupled parallel sub-super solutions. The results obtained in this paper essentially improve the famous Amann three-solution theorem. As applications, a second order system of differential equations is considered. Cited in 2 Documents MSC: 47J05 Equations involving nonlinear operators (general) 34B15 Nonlinear boundary value problems for ordinary differential equations 47H10 Fixed-point theorems 47N20 Applications of operator theory to differential and integral equations Keywords:fixed point index; multiple solutions; parallel sub-super solutions PDFBibTeX XMLCite \textit{K. Zhang} and \textit{J. Sun}, Acta Math. Sin. 48, No. 1, 99--108 (2005; Zbl 1117.47304)