An extension of Leggett-Williams norm-type theorem for coincidences and its application

Aijun Yang

Abstract


In this paper, several versions extension of
Leggett-Williams norm-type theorem for coincidences are given and
proved to obtain the positive solutions of the operator equation
$Mx=Nx$, where $M$ is a quasi-linear operator and $N$ is nonlinear.
Moreover, as an application, the existence of positive solutions for
multi-point boundary value problem with a $p$-Laplacian is obtained
by one of those theorems.

Keywords


Boundary value problem; resonance; cone; positive solution; coincidence

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