We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness of generalized stochastic flows. Moreover, we also prove the existence and uniqueness of L-solutions or measure-valued solutions for second order integro-differential equation of Fokker-Planck type.

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

In this paper, we research the existence and uniqueness of positive solutions for a coupled system of fractional differential equations. By means of some standard fixed point principles, some results on the existence and uniqueness of positive solutions for coupled systems are obtained.

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. c © 2006 Elsevier Ltd. All rights reserved.

This paper presents criteria for the existence and uniqueness of solutions to five-point boundary value problems associated with third order differential equations by using matching technique. ’Liapunov-like’ functions are used as a tool to establish existence and uniqueness of solutions by matching two three-point boundary value problems. AMS Mathematics Subject Classification (2000): 34B10, 3...

This work formulates existence, uniqueness and uniqueness implies existence theorems for solutions to two-point vector boundary value problems on time scales. The methods used include maximum principles, a priori bounds on solutions and the nonlinear alternative of Leray-Schauder. AMS Subject Classification: 39A12