Related papers: Integrable solutions of a generalized mixed-type f…
In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
In this paper, we will show that if for every nonlinear complex irreducible character of a finite group G, some multiple of it is induced from an irreducible character of some proper subgroup of G, then G is solvable. This is a…
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…
Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the approaches to study them is, firstly, to find formal solutions…
The generalized sine-Gordon (sG) equation $u_{tx}=(1+\nu\partial_x^2)\sin\,u$ was derived as an integrable generalization of the sG equation. In a previous paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is referred to…
We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)
In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability for the quadratic type functional equation &f(x+y+2cz)+f(x+y-2cz)+c^2f(2x)+c^2f(2y) &=2[f(x+y)+c^2f(x+z)+c^2f(x-z)+c^2f(y+z)+c^2f(y-z)] {2.6 cm}…
The sufficient conditions are obtained for existence of the main solution of the nonlinear Volterra integral equation of the second kind on the semi-axis and on a finite interval. The method for computation of this boundary interval is…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $F\colon I\times E\map E$ with weakly sequentially closed graph, we consider the…
We introduce a special type of dissipative Ermakov-Pinney equations of the form v_{\zeta \zeta}+g(v)v_{\zeta}+h(v)=0, where h(v)=h_0(v)+cv^{-3} and the nonlinear dissipation g(v) is based on the corresponding Chiellini integrable Abel…
In the present paper, we consider the solvability of positive solutions of nonlinear integral equations by means of investigating non-linear Markov operators. To solve the problem we find necessary and sufficient condition for the…
We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,d\xi_T(s)$, $t\ge0$, as $T\to\infty$. Here $\xi_T(t)$ is a strong solution of the stochastic differential equation…
Integral equations of the form $$ x(t)=x(t_0)+\int_{t_0}^t d[A]\,x=f(t)-f(t_0)$$ are natural generalizations of systems of linear differential equations. Their main goal is that they admit solutions which need not be absolutely continuous.…
A comprehensive algebro-geometric integration of the two component Nonlinear Vector Schr\"odinger equation (Manakov system) is developed. The allied spectral variety is a trigonal Riemann surface, which is described explicitly and the…
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.
We prove that the superlinear indefinite equation \begin{equation*} u" + a(t)u^{p} = 0, \end{equation*} where $p > 1$ and $a(t)$ is a $T$-periodic sign-changing function satisfying the (sharp) mean value condition $\int_{0}^{T} a(t)~\!dt <…
In our preceding paper, we have proposed an algorithm for obtaining finite-norm solutions of higher-order linear ordinary differential equations of the Fuchsian type [\sum_m p_m (x) (d/dx)^m] f(x) = 0 (where p_m is a polynomial with…