Boundary-value problems for nonautonomous nonlinear systems on the half-line

Electronic Journal of Differential Equations

关键词: Ordinary differential equation;    half-line;    infinite interval;    boundary and initial value problem;    Fredholm operator;    degree theory;    exponential dichotomy;    properness;    a priori bounds;   

DOI  :  

来源: DOAJ

【 摘 要 】

A method is presented for proving the existence of solutions forboundary-value problems on the half line. The problems under studyare nonlinear, nonautonomous systems of ODEs with the possibilityof some prescribed value at $t=0$ and with the condition thatsolutions decay to zero as $t$ grows large. The method reliesupon a topological degree for proper Fredholm maps.Specific conditions are given to ensure that the boundary-valueproblem corresponds to a functional equation that involves anoperator with the required smoothness, properness, and Fredholmproperties (including a calculable Fredholm index).When the Fredholm index is zero and the solutions are boundeda priori, then a solution exists. The method is appliedto obtain new existence results for systems of the form$dot{v}+g(t,w)=f_1(t)$ and $dot{w}+h(t,v)=f_2(t)$.

【 授权许可】

Unknown