Several Types Of Equations Of Positive Solutions And Blow

Multi-point boundary value problems is an important branch of differential equation theory, it has profound theoretical physics background and a wide range of applications. For some time there has been much of a wide range of research methods they use to study the nonlinear functional analysis Been more positive solution on the existence of a large number of results. Also on the exact number of solutions of problems, and solutions blow-up in a finite time, is also a very important issue. This problem of these three areas are covered.The thesis is divided into three chapters according to the contents.In Chapter 1, using the Krasnosel'skill fixed point theorem, we establish the existence result of positive solutions for the following nth-order infinity-point boundary value problem involing the operator of p-Laplacian where d> 0,& G (0,1), ai∈[0,∞), (?)*i&< 1, A> 0, a G C([0,1], [0,∞)), and f∈C([0,∞),[0,∞)).In Chapter 2, using shoting methord, we establish the exact number of positive solutions for the following two-point boundary value problem involing the operator of p-LaplacianIn Chapter 3, by integral equalities and multiplier techniques, we considered a nonlinear viscoelastic hyperbolic equation of a more general form where X is a Hilbert space, A:D(A) (?) Xâ†'X is an accretive self-adjoint linear operator, and F denotes the gradient of a Gateaux differentiable function F:D(?)Aâ†'R, and p> max{k, r}> 1.Ωis a bounded domain of Rn, with a smooth boundary dΩand a unit outer normal v. On the condition of supporting that the solution is exist firstly, then a blow-up result is obtained.