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Multiple solutions for superlinear operator equations in Banach spaces and applications. (Chinese. English summary) Zbl 1117.47304

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.

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
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