The Existence Of Positive Solutions For Boundary Value Problems With Integral Boundary Conditions

Boundary value problems with integral boundary conditions have their wide applications. In applied mathematics and physics, such as thermal conductivity, semiconductor, chemical burn, groundwater flow, many boundary conditions of heat elasticity and dynamic problems can be attributed to the integral boundary conditions. In this paper, we mainly study the existence of positive solutions for several classes of boundary value problems with integral boundary value problems.In the second chapter, we are concerned with the existence of positive solutions for the following singular second order multi-point boundary value problem with integral boundary condition: The arguments are based upon a specially constructed cone and the fixed point theorem of cone expansion-compression type. Meanwhile, an example is given to demonstrate the main results.In the third chapter, we consider positive solutions for a class of three-point singular boundary value system with a p-Laplacian operator and some integral boundary condition, where the system is By using the fixed point theorem, under appropriate conditions, we obtain the sufficient conditions for the existence of one、two or three positive solutions about this class of boundary value problems, and give two examples to illustrate our results.In the forth chapter, the positive solutions of the following second order impulsive differential equation with integral boundary conditions are considered:By introducing a piecewise function for variable substitution, we transformation the impulsive differential equation into an integral equation, and then use the fixed point theorem, we prove the existence of positive solutions of above boundary value problems under some suitable conditions.