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We consider the following system of differential equations
,
,
We apply a fixed point result for multifunctions to derive existence results for boundary value problems of Sturm-Liouville differential equations with nonlinearities that may involve discontinuous and functio...
We give a Grüss-type inequality which is a refinement of a result due to Dragomir and Agarwal. We also give its applications for the moments of random variables, guessing mappings, and Ozeki's inequality.
We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implic...
By use of the concavity of solution for an associate boundary value problem, existence criteria of positive solutions are given for the Dirichlet BVP
Let
be a strictly increasing sequence of natural numbers and let
be a space ...
We introduce and study a new class of generalized nonlinear variational-like inequalities, which includes these variational inequalities and variational-like inequalities due to Bose, Cubiotti, Dien, Ding, Din...
One-dimensional Hardy inequalities with weights and remainder terms are studied. The corresponding optimal constants are discussed. Then by the process of symmetrization, Hardy inequalities with remainder term...
The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. W...
We establish optimal, in a sense, unique solvability conditions of the Cauchy problem for a wide class of linear functional differential equations in a Banach space with a solid wedge. The conditions are formu...
We study Carrier's equation in a noncylindrical domain. We use the penalty method combined with Faedo-Galerkin and compactness arguments. We obtain results of the existence and uniqueness of the local solution.
We consider a natural correspondence between a family of inequalities and a closed convex set. As an application, we give new types of power mean inequalities and the Hölder-type inequalities.
We first prove local weighted Poincaré-type inequalities for differential forms. Then, by using the local results, we prove global weighted Poincaré-type inequalities for differential forms in John domains, wh...
For the linear delay difference system
, where
is a
...
We investigate the global asymptotic behavior of solutions of the system of difference equations
,
...
The classical Bernstein pointwise estimate of the (first) derivative of a univariate algebraic polynomial on an interval has natural extensions to the multivariate setting. However, in several variables the do...
We prove some common fixed point theorems for left reversible and near-commutative semigroups in compact and complete metric spaces, respectively. As applications, we get the existence and uniqueness of soluti...
The well-known Krasnoselskii twin fixed point theorem is used to investigate the existence of mild solutions for first- and second-order impulsive semilinear functional and neutral functional differential equa...
A general method is given in order to guarantee at least one nontrivial solution, as well as infinitely many radially symmetric solutions, for an abstract class of hemivariational inequalities. This abstract c...
We establish optimal, in a sense, conditions under which, for arbitrary forcing terms from a suitable class, a linear inhomogeneous functional differential equation in a preordered Banach space possesses solut...
We develop an inequality for the expectation of a product of
random variables generalizing the recent work of Dedecker and Doukhan (2003) and th...
The new extension of the weighted Montgomery identity is given by using Fink identity and is used to obtain some Ostrowski-type inequalities and estimations of the difference of two integral means.
We will prove the Hyers-Ulam stability of the Butler-Rassias functional equation following an idea by M. T. Rassias.
Let
denote the space of all holomorphic functions on the unit ball
. In this ...
We consider a prototype of quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalizati...
-harmonic tensors
We prove Poincaré-type estimates involving the Hodge codifferential operator and Green's operator acting on conjugate
-harmonic tensors.
We give a refinement of the Poincaré inequality for Kolmogorov operators on
. This refinement yields some regularity result of the corresponding ...
The inequality discovered by L. K. Hua in 1965 has been generalized in several directions. In this paper, we adopt a certain conjugate method to give a simple and fundamental inequality on two functions on a s...
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