Related papers: Regularity theory for nonlinear integral operators
Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…
In this paper we use the dynamical methods to establish the existence of nontrivial solution for a class of nonlocal problem of the type $$ \left\{\begin{array}{l} -a\left(x,\int_{\Omega}g(u)\,dx \right)\Delta u =f(u), \quad x \in \Omega \\…
The class of nonlinear integral equations on the positive half-line with a monotone operator of Hammerstein type is studied. With various partial representations of the corresponding kernel and nonlinearity, this class of equations has…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
We revisit the regularity theory for uniformly elliptic equations.
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to…
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear nonlocal setting. First of all, we prove that weak solutions to a class of homogeneous nonlinear nonlocal equations of possibly arbitrarily low…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
In this work we study integral equations defined on the whole real line. Using a suitable Banach space, we look for solutions which satisfy some certain kind of asymptotic behavior. We will consider spectral theory in order to find fixed…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schr\"odinger equations. We also sketch an application to nonlinear optics and discuss some open problems.
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a…
By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…