Sahiner, Y.
Zafer, Ağacık
By using a technique similar to the one introduced by Kong [J Math Anal Appl 229 (1999) 258-270] and employing an arithmetic-geometric mean inequality, we establish oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form


Solving Fokker-Planck Equation By Two-Dimensional Differential Transform
Cansu Kurt, Ümmügülsüm; Ozkan, Ozan (2011-07-29)
In this paper, we implement a reliable algorithm to obtain exact solutions for Fokker-Planck equation and some similar equations. The approach rests mainly on two dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions are obtained easily without linearizing the problem. Some illustrative examples are given to demonstrate the effectivene...
Inverse problems for a semilinear heat equation with memory
Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005)
In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities
Agarwal, Ravi P.; Zafer, A. (Springer Science and Business Media LLC, 2009)
We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r(t)Phi(alpha)(x(Delta)))(Delta) + f(t,x(sigma)) = e(t), t is an element of [t(0), infinity)(T) with f (t, x) = q(t) Phi(alpha)(x) + Sigma(n)(i=1)q(i)(t)Phi(beta i)(x), Phi(*)(u) = vertical bar u vertical bar*(-1) u, where [t(0), infinity)(T) is a time scale interval with t(0) is an element of T, the functions r, q, q(i), e : [t(0), infinity)(T) -> R are right-dense contin...
Differential equations on variable time scales
Akhmet, Marat (2009-02-01)
We introduce a class of differential equations on variable time scales with a transition condition between two consecutive parts of the scale. Conditions for existence and uniqueness of solutions are obtained. Periodicity, boundedness and stability of solutions are considered. The method of investigation is by means of two successive reductions: B-equivalence of the system [E. Akalfn, M.U. Akhmet, The principles of B-smooth discontinuous flows, Computers and Mathematics with Applications 49 (2005) 981-995; ...
Generalisation of the Lagrange multipliers for variational iterations applied to systems of differential equations
ALTINTAN, DERYA; Uğur, Ömür (2011-11-01)
In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses restricted variations only for nonlinear terms by generalising the Lagrange multipliers. Consequently, this allows us t...
Citation Formats
A. F. GÜVENİLİR, Y. Sahiner, and A. Zafer, “MIXED NONLINEAR OSCILLATION OF SECOND ORDER FORCED DYNAMIC EQUATIONS,” DYNAMIC SYSTEMS AND APPLICATIONS, pp. 635–649, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56071.