For a class of operator inclusions with multivalued terms fulllling mixed semicontinuity hypotheses, the existence of solutions is established by chieey using Bressan and Colombo's directionally continuous selection theorem as well as Ky Fan's xed point principle. An application to the Cauchy problem is then performed.

Analytic solutions for Burgers equations with source terms, possibly stiff, represent an important element to assess numerical schemes. Here we present a procedure, based on the characteristic technique to obtain analytic solutions for these equations with smooth initial conditions.

In this paper, the solution of linear second order equations with fuzzy initialvalues are investigated. The analytic general solutions of them using a rstsolution is founded. The parametric form of fuzzy numbers to solve the secondorder equations is applied. The solutions are searched in four cases. Finallythe example is got to illustrate more and the solutions are shown in gures forfour cases.

Maximum likelihood (ML) is increasingly used as an optimality criterion for selecting evolutionary trees, but finding the global optimum is a hard computational task. Because no general analytic solution is known, numeric techniques such as hill climbing or expectation maximization (EM), are used in order to find optimal parameters for a given tree. So far, analytic solutions were derived only ...

There is no general existence theorem for solutions for nonlinear difference equations, so we must prove the existence of solutions in accordance with models one by one. In our work, we found theorems for the existence of analytic solutions of nonlinear second order difference equations. The main work of the present paper is obtaining representations of analytic general solutions with new metho...