Some remarks on a fixed point theorem of Krasnoselskii [PDF]
, 2003 Using a particular locally convex space and Schaefer's theorem, a generalization of Krasnoselskii's fixed point Theorem is proved. This result is further applied to certain nonlinear integral equation proving the existence of a solution on $\mathbb{R}_{+}
Avramescu, C.
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Polynomial solutions of nonlinear integral equations [PDF]
, 2008 We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.Comment: 10 ...
Andrews G E +5 more
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Global attractors for nonlinear viscoelastic equations with memory [PDF]
, 2013 We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos.
Conti, Monica +2 more
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Discrete Modified Projection Methods for Urysohn Integral Equations with Green's Function Type Kernels [PDF]
, 2019 In the present paper we consider discrete versions of the modified projection methods for solving a Urysohn integral equation with a kernel of the type of Green's function. For $r \geq 0,$ a space of piecewise polynomials of degree $\leq r $ with respect
Kulkarni, Rekha P., Rakshit, Gobinda
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Decay estimates for nonlinear nonlocal diffusion problems in the whole space [PDF]
, 2013 In this paper we obtain bounds for the decay rate in the $L^r (\rr^d)$-norm for the solutions to a nonlocal and nolinear evolution equation, namely, $$u_t(x,t) = \int_{\rr^d} K(x,y) |u(y,t)- u(x,t)|^{p-2} (u(y,t)- u(x,t)) \, dy, $$ with $ x \in \rr^d$, $
Antolin, Angel San +3 more
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Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations [PDF]
, 2008 In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases when the normal velocity depends on the moving front in a ...
Alvarez +20 more
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Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence
Advances in Nonlinear Analysis, 2014 We consider the following problem: given a bounded convex domain Ω⊂ℝN${\Omega \subset \mathbb {R}^N}$ we consider the limit as p → ∞ of solutions to -div(bp-p|Du|p-2Du)=f+-f-${- \operatorname{div} (b_{p}^{-p} |Du|^{p-2} Du)=f_+ - f_-}$ in Ω and bp-p|Du|p-
Mazón José M. +2 more
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Solving some nonlinear equations by successive approximations
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 6, Page 353-358, 2002., 2002 The iterations scheme generated by an infinite sequence of operators satisfying some contractive conditions in a complete metric space is used to solve some integral equations of Hammerstein type.
Albert K. Kalinde
wiley +1 more source
Volterra and Urysohn integral equations in Banach spaces
International Journal of Stochastic Analysis, Volume 11, Issue 4, Page 449-464, 1998., 1997 We use topological methods to present existence principles and theory for integral equations in Banach spaces.
Donal O′Regan
wiley +1 more source
Exotic dynamics in a firing rate model of neural tissue with threshold accommodation [PDF]
, 2007 Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity.
Coombes, Stephen, Owen, Markus R.
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