Leggett-williams - Open Access .click

Archiv Der Mathematik, 2006
We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the ...
Donal O'Regan, Mirosława Zima
exaly +2 more sources

Leggett–Williams theorems for coincidences of multivalued operators

Nonlinear Analysis: Theory, Methods & Applications, 2008
Let \(X,Y\) be Banach spaces, \(C\) be a cone in \(X\) and let \(\Omega_1,\Omega_2\) be open bounded subsets of \(X\) with \(\overline{\Omega}_1\subset\Omega_2\). For a pair \((L,N)\) consisting of a linear Fredholm operator \(L:\text{dom}\,L\subset X\to Y\) of zero index and an upper semicontinuous (compact convex)-valued multimap \(N:X\multimap Y ...
Donal O'Regan, Mirosława Zima
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Leggett–Williams type theorems with applications to nonlinear differential and integral equations

Nonlinear Analysis: Theory, Methods & Applications, 2015
The authors generalize several results of \textit{R. W. Leggett} and \textit{L. R. Williams} [J. Math. Anal. Appl. 60, 248--254 (1977; Zbl 0352.45005)]. In particular, they consider a class of maps which are more general than the compact ones in an ordered Banach space.
Dariusz Bugajewski, Piotr Kasprzak
exaly +2 more sources

mathematics
fixed-point theorems
cone

positive solution
fixed point theorem
positive solutions

boundary value problem
compression
expansion