Global Structure Of Solutions For Prescribed Curvature Equations In Euclidean Space

In this thesis,by using the Rabinowitz’s global bifurcation theorem,we s-tudy the existence and global structure of positive solutions for a.one-dimensional prescribed curvature equations in Euclidean space,by using the Leray-Schauder fixed point tlheorem study tho existence of radial positive solutions for a prescribed curvature problem in Euclidean space.We describe them in detail as follows.1.By using Rabinowitz’s Global bifurcation theorem,we study the existence and global structure of positive solutions for the one-dimensional prescribed curva-ture equation(?)where λ>0 is a parameter,f∈C((0,∞),(0,∞)).under conditional:k1S ≤f(s)≤k2S and k1 ≤ f0 ≤ k2,we obtained the existence and global structure of positive solutions;the limits f0:=(?)The main results extend the corresponding of S.Casanova,J.Lopez-Gomez and Takinmoto[J.Differential Equations.,2012].2.By using Lcray-Schauder fixed point theorem,wo study the existence of positive radial solutions for the prescribed curvature problem in Euclidean space(?)where λ>0 is a parameter.B(b)= {x∈RN:|x|＜ b},a:[0,b]→ R is signed,f:[0,∞)→ R is continued,s∈[0,b],f(s)>0.we obtained there exists a positive number A*such that(P2)has a positive solution for λ(0,λ*).The main results extend the corresponding of D.D.Hai[Nonlinear Anal.,1998].