Existence of Solutions of General Nonlinear Stochastic Volterra Fredholm Integral Equations

Abstract In this paper, we establish a set of sufficient conditions for the existence of solutions of nonlinear Volterra-Fredholm stochastic integral equations by using the notion of measure of noncompactness and the Darbo fixed point theorem.

[1]  V. Rao.  On random solutions of Volterra-Fredholm integral equations , 1983 .

[2]  W. J. Padgett,et al.  Almost surely continuous solutions of a nonlinear stochastic integral equation , 1976, Mathematical systems theory.

[3]  Jözef Banai,et al.  MEASURES OF NONCOMPACTNESS IN THE SPACE OF CONTINUOUS TEMPERED FUNCTIONS , 1981 .

[4]  W. J. Padgett,et al.  On a Class of Stochastic Integral Equations of Mixed Type , 1977, Inf. Control..

[5]  D. Szynal,et al.  On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy , 1988, Journal of Applied Probability.

[6]  Random contractors with random nonlinear majorant functions , 1979 .

[7]  W. J. Padgett,et al.  A new stochastic formulation of a population growth problem , 1973 .

[8]  K. Balachandran,et al.  Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy , 1999, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[9]  W. J. Padgett,et al.  Solution of a Stochastic Integral Equation Using Integral Contractors , 1979, Inf. Control..

[10]  W. J. Padgett,et al.  On random nonlinear contractions , 1977, Mathematical systems theory.

[11]  D. Szynal,et al.  On existence and asymptotic behaviour of solutions of a nonlinear stochastic integral equation , 1985 .

[12]  Chris P. Tsokos,et al.  On a stochastic integral equation of the Volterra type , 1969, Journal of Applied Probability.

[13]  Existence of a Solution of a Stochastic Integral Equation in Turbulence Theory , 1971 .

[14]  W. J. Padgett,et al.  Random integral equations with applications to stochastic systems , 1971 .

[15]  A random Fredholm integral equation , 1972 .

[16]  W. J. Padgett,et al.  Random contractors and the solution of random nonlinear equations , 1977 .

[17]  H. Onose.  On the Boundedness of Random Solutions of Nonlinear Stochastic Integral Equations , 1986 .

[18]  C. Tsokos,et al.  On the existence of random solutions of a non-linear perturbed random integral equation , 1978 .

[19]  D. Szynal,et al.  ON SOLUTIONS OF SOME NONLINEAR STOCHASTIC INTEGRAL EQUATIONS , 1993 .

[20]  Chris P. Tsokos,et al.  Random integral equations with applications to life sciences and engineering , 1974 .