Continuous solutions of a linear homogeneous functional equation

The Continuous Solutions of a Generalized Dhombres Functional Equation

We consider the functional equation f(xf(x)) = φ(f(x)) where φ : J → J is a given increasing homeomorphism of an open interval J ⊂ (0,∞) and f : (0,∞) → J is an unknown continuous function. In a series of papers by P.Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under φ and which contains in its interior no fixed point e...

Non-trivial periodic solutions of a non-linear Hill’s equation with positively homogeneous term

The existence of non-trivial periodic solutions of a general family of second order differential equations whose main model is a Hill’s equation with a cubic nonlinear term arising in different physical applications is proved. c © 2005 Elsevier Ltd. All rights reserved.

Continuous Solutions of Linear Equations

Exact solutions of a linear fractional partial differential equation via characteristics method

‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...

Short solutions for a linear Diophantine equation

It is known that finding the shortest solution for a linear Diophantine equation is a NP problem. In this paper we have devised a method, based upon the basis reduction algorithm, to obtain short solutions to a linear Diophantine equation. By this method we can obtain a short solution (not necessarily the shortest one) in a polynomial time. Numerical experiments show superiority to other method...