Let V be a nonnegative locally bounded function defined inQ∞ := R × (0,∞). We study under what conditions on V and on a Radon measure μ in R does it exist a function which satisfies ∂tu−∆u+ V u = 0 in Q∞ and u(., 0) = μ. We prove the existence of a subcritical case in which any measure is admissible and a supercritical case where capacitary conditions are needed. We obtain a general representat...

This paper deals with a problem of conservation of energy in a singular initial value problem. These kind of problems appear in the study of radially symmetric elliptic and hyperbolic boundary value problems. The interesting question that arises is how to analyze the oscillation of the solutions, count the number of nodes and estimate their location. In order to conduct the analysis we need to ...

In this paper, Laplace Decomposition Method (LDM) which is coupling of Laplace Transform (LT) and Adomian’s Decomposition Method (ADM) is employed to construct the exact solution of two mathematical problems which arises in diverse fields of physics. It has been observed that this proposed coupling is very efficient and reliable for the solution of the nonlinear problems. Numerical results and ...

  In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems    

A new implicit method has been presented for solving singular initial value problems. The formula has derived in such a way that it excludes the singular point. The method is illustrated by suitable examples (first and second order). To check the results the approximate solutions have been compared to exact solutions KeywordsSingular initial value problems; Lane-Emden equations; Emden-Fowler eq...