Positive Solutions Of A Class Of Strong Coupling Systems Describing Suspension Bridge

In this thesis,by using the fixed point index theory,we study the existence and multiplicity of positive solutions of a class of strong coupling systems of second and fourth-order ordinary differential equations.We describe them in detail as follow.1.We prove the existence of positive solutions of strong coupling systemwhere f,g:[0,+?)×[0,+?)?[0,+?)are continuous.We show the existence of positive solutions under the assumptionsl(?),(?),where |(u,v)|=max{|u|,|v|,or(?)f,g are bounded functions,or(?)g is bounded and f is unbounded and(?),or(?)g is increasing in each variable for any value of the other variable,f is unbounded,at same time,the following is satisfied(?),or(?)f is bounded and g is unbounded and(?),or f is increasing in each variable,(?)g is unbounded,and(?).2.We prove the existence of positive solution of the strong coupling systems witjh parameter,where ?>0 is a parameter,f,g:[0,+?)×[0,+?)?[0,+?)are continuous and f(u,v),g(u,v)are strictly increasing in each variable for any value of the other variable.3.We consider the existence aid multiplicity of positive solutions for strong coupling systems with two parametersWhere ? and ? are parameters,f,g:[0,?)×[0,?)?[0,?)are continuous and f(0,0)>0,g(0,0)>0,for u,v>0.We show the existence of at least one positive couple solution under assumptions(a)f0=g0=0 and either f?=?,org?=?,(b)f?=g?=0 and either f0=?,org0=?.And show the existence of at least two positive couple solutions under assumptions(a)f0=g0=f?=g?=0,(b)either f0=?,org0=?,and either f?=?,org?=?.