Solvability Of Boundary Value Problem For A Class Of Fully Second-Order Integro-Differential Equations

This thesis discusses the solvability of boundary value problem for fully second-order integro-differential equations (?) where f:[0,1] × R4 → R is a continuous function, T, S are Volterra and Fredholm type integral operators.Under the condition that f satisfies some inequalities,the results of existence and uniqueness of solutions and the existence of positive solutions for this problem are obtained by respectively using the Leray-Schauder fixed point theorem,method of upper and lower solutions and the fixed point index theory on cones,the results are applied to special boundary value problem to second-order integro-differential equations,and conclusions about the new existence of solutions are reached.The main results are as follows:1.Under the conditions that the nonlinear term f(t,x,y,z,p)satisfies the one-sided super-linear growth and Nagumo-type growth on y,the existence and uniqueness of solutions for fully second-order integro-differential equation boundary value problems are obtained by using the Leray-Schauder fixed point theorem,some results of literature are generalized.2.Under the condition that the derivative term of the nonlinear term f(t,x,y,z,p)about the unknown function satisfies the Nagumo-type growth,the existence of solutions for fully second-order integro-differential equation boundary value problems are obtained by using the method of upper and lower solution and the truncation function technique,some results of literature are generalized.3.Constructing a convex closed cone and by using the fixed point index theory on cones,under the condition that the nonlinear term f(t,x,y,z,p)about x,y,z and p satisfy the super-linear or sub-linear growth,the existence of positive solutions for fully second-order integro-differential equation boundary value problems are obtained,some results of literature are generalized.