In this paper we establish some results for asymptotic linear Hammerstein integral equations. Using Morse theory and in particular critical groups we prove a number of existence results.
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The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel'skiĭ's fixed point theorem due to Nashed and Wong are used to establish existence of $L^α$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.
New fixed point results are presented for maps defined on closed subsets of a Fréchet space \(E\). The proof relies on fixed point results in Banach spaces and viewing \(E\) as the projective limit of a sequence of Banach spaces.
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We present a Furi-Pera type theorem for weakly sequentially continuous maps. As an application we establish new existence principles for elliptic Dirichlet problems.
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The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.
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The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.
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In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.
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We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.
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