The Radial Solution Of The Semipositone Problem On The Outer Region Of The Sphere

The thesis mainly studies the existence of solutions of nonlinear elliptic equations with several methods of nonlinear functional analysis.The thesis consists of four chapters.In the first chapter,we mainly introduce the background and development of domestic and foreign research,and give the main research work of this paper.In the second chapter,we consider the solution of elliptic equation.On the right line by using the theory of compressed image combined with weighted norm analysis technique,in mild conditions,we got the class of problems has at least a positive radial solution.In the third chapter,we mainly study the equation:-?z ??G(| t |)g(z).t ??.?>0.? = {t? RN:| t |>r0,rO>0,N>2}.? is the Laplacian operator,G ?C([r0,?),(0,?)satisfies G(r)?1/rN+v;v>for r>>1 and g ?C1([0,?),R)is a concave increasing function satisfying lims??g(s)/s=0 and g(0)<0.We used the principle of maximum and minimum values to discussed the solutions z such that z?0 as | t |?? and satisfy the linear boundary condition a/a? = 0 where az/? is the outward normal derivative.We will establish the uniqueness of positive radial solutions for large values of the parameter ?.Namely,We study positive radial solutions to:the uniqueness solutions and for its application of the extension of the half line problem.In chapter four,we present a class of elliptic equations,and the existence of radi-al positive solutions of schrodinger equation is established by using nonlinear functional analysis techniques.