Abstract
AbstractIn Chap. 6, on superlinear systems of Hammerstein integral equations and applications, we use the Leray–Schauder degree to obtain new results on the existence of solutions, and apply them to two-point boundary problems of systems of equations. We also are concerned with the existence of (component-wise) positive solutions for a semilinear elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing a cone K 1×K 2, which is the Cartesian product of two cones in the space \(C(\overline{\Omega})\), and computing the fixed point index in K 1×K 2, we establish the existence of positive solutions for the system.KeywordsFixed Point IndexSemilinear Elliptic SystemsHammerstein Integral EquationsLeray-Schauder DegreeSublinearThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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