Abstract
Based on the fixed point index and partial order method, one new order-type existence theorem concerning cone expansion and compression is established. As applications, we present sufficient existence conditions for the first- and second-order periodic problems. MSC: 34B15
Highlights
Introduction and preliminaries LetX, Y be real Banach spaces
In [ ], Cremins established a fixed point index for A-proper semilinear operators defined on cones which includes and improves the results in [, ]
2 An abstract result We will establish an abstract existence theorem concerning cone expansion and compression of order type, which reads as follows
Summary
Introduction and preliminaries LetX, Y be real Banach spaces. Consider a linear mapping L : dom L ⊂ X → Y and a nonlinear operator N : X → Y. In [ ], Cremins established a fixed point index for A-proper semilinear operators defined on cones which includes and improves the results in [ , , ]. We will use the properties of the fixed point index in [ ] and partial order to present a new order-type existence theorem concerning cone expansion and compression which extends the corresponding results in [ ].
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