Related papers: Some linear and nonlinear integral inequalities on…
In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing…
In this paper, we establish new an inequality of weighted Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
By the coupling method, we establish the Harnack inequalities, derivative formula and Driver's integration by parts formula for the stochastic Klein-Gordon type equations in the interval. We provide a detailed discussion about the nonlinear…
The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
In this work, initial-boundary value problems for the time-fractional Airy equation are considered on different intervals. We study the properties of potentials for this equation and, using these properties, construct solutions to the…
In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…
The main objective of this paper is to study some Ostrowski and Trapezoid type inequalities for double integrals on Time Scales. Some other interesting inequalities are also given.
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
We study an eigenvalue problem in the framework of double phase variational integrals and we introduce a sequence of nonlinear eigenvalues by a minimax procedure. We establish a continuity result for the nonlinear eigenvalues with respect…
This paper presents an approach for obtaining approximate solutions to quasi-variational inequalities in a real Hilbert space by modifying Tseng's scheme, which was originally designed for variational inequalities. The study explores the…
We give sufficient conditions on the initial data so that a semilinear wave inequality blows-up in finite time. Our method is based on the study of an associated second order differential inequality. The same method is applied to some…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable in the sense that they are realisable as Fredholm Grassmannian flows. In other words, time-evolutionary solutions to such…
In this paper we prove the Fractional Gagliardo-Nirenberg Inequality, Polya-Szego Inequality and the Sharp Fractional Sobolev Inequality, we then provide an application of such inequalities in a constraiend variational problem involving the…
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The…