Existence Of Positive Solutions For Several Classes Of Juvenile-adult Models

In this dissertation,we study the existence of multiple positive solutions of Juvenile-adult models with general nonlinear terms and the existence of positive solutions of generalized population model with Neumann and Dirichlet boundary conditions respectively by using the methods of Rabinowitz global bifurcation theory,connected branch taking limit,upper and lower solution methods,exponential jump principle,etc.The main work is as follows:1.We study the existence of multiple positive solutions of the following Juvenile-adult models with general nonlinear terms (?) where ? is a positive parametar,? is a bounded regular domain of Rn(n>1),?is an n-dimensional compact connected smooth submanifold of Rn with boundary(?)?.the coefficients a,b,c,d,?and? are continuous differentiable positive function,fi?C(R+2,R+)(R+=[0,?),R+2=R+×R+),i=1,2.The main results of this section generalize the related work of Arino and Montero[proc.Edinburgh math.SOC.2000],Canada et al.[J.math.Anal.Appl.2001].2.We study the existence of positive solutions with generalized population mod-el with Neumann boundary conditions (?) where ? is a bounded regular domain of Rn(n>1),? is an n-dimensional compact connected smooth submanifold of Rn with boundary (?)?,? denotes the outer unit normal vector on the boundary (?)? of region ?.The coefficients a,b,c,d,e,f,g,h,p,?,?,? are continuous differentiable positive function,fi?C(R+3,R+)(R+=[0,?),R+3=R+×R+×R+),i=1,2,3.The main difficulties to be overcome in this section are:the number of equations increases from two to three,resulting in a large number of calculations.when the number of equations decreases from three to two,(Q2)degenerates into the work of Brown and Y.Zhang[J.math.Anal.Appl.2003],Bouguima et al.[nonliner anal.RWA 2008].Therefore,the main results in this section generalize their main conclusions.3.We study the existence of positive solutions for generalized population model with Dirichlet boundary conditions (?) where ? is a bounded regular domain of Rn(n>1),? is an n-dimensional compact connected smooth submanifold of Rn with boundary(?)?,the coefficients a,b,c,d.e,f g,h,p,?,? and ? in C?(?)(0<?<1)are continuous differentiable positive function,fi?Cu(R+3,R+)(R+=[0,?),R+=R+x R+x R+)),i=1,2,3When W(x)? 0,x??(Q3)degenerates into the related work of R.Ma and R.Chen[Appl.Math.Comput.2014],so their work is promoted.