The Existence Of Solutions To Two Classes Of P-laplacian Operator Boundary Value Problems

As we all know,nonlinear functional analysis is used in the study of medicine,biology,classical and modern physics and economics.There are three main sources of nonlinear functional analysis: differential geometry problem,variational problems associated with nonlinear second functional,mathematical problems in classical and modern physics.Moreover,new nonlinear mathematical problems have been proposed in the fields of genetics,economics and biology.Nonlinear functional analysis is an important branch of modern analytical mathematics,it has become one of the important research directions in modern mathematics.It is also an important and powerful tool for dealing with very many nonlinear problems,it plays an irreplaceable role in the study of nonlinear differential equations and partial differential equations.The boundary value problems of nonlinear differential equation is derived from various application courses.For example,biology,boundary layer theory,gas dynamics,nuclear physics,fluid mechanics,nonlinear optics,etc.The boundary value problem of differential equation is very important in theory and practical application,in recent decades,many mathematicians use the topological degree method in nonlinear functional analysis to solve boundary value problems of nonlinear differential equations,especially the existence of positive solutions,and many important results have been achieved.But the boundary value problem of the second order ordinary differential equation with p-laplacian operator first emerged in the study of gas turbulence in non-newtonian mechanics and porous media [1,2,3] about in the late 1980 s and early 1990 s.Then,this problem is involved in the study of glaciological combustion theory and nonlinear elastic mechanics,biology [4] and a variety of nonlinear fluids [5,6] and the partial differential equations with p-laplacian operator.On the other hand,because in the process of solving practical problems,especially in the research of modern physics,more and more differential equations with p-laplacian operator or p(x)-Laplacian operator have emerged,has been continuously injected the research on this issue with new vitality.Because of its wide application background,it has become a hot topic of research,see articles[7,8,9].In thispaper,we use the relevant fixed point theorem and the sufficient conditions for positive solutions of two boundary value problems with p-laplacian operators are obtained.Popularize and enrich previous literature results.