On the Solution of Hammerstein Integral Equations with Loads and Bifurcation Parameters

Abstract

The Hammerstein integral equation with loads on the desired solution is considered. The equation contains a parameter for any value of which the equation has a trivial solution. Necessary and sufficient conditions are obtained for the coefficients of the equation and those values of the parameter (bifurcation points) in its neighborhood the equation has a nontrivial real solutions. The leading terms of the asymptotics of such branches of solutions are constructed. Examples are given illustrating the proven existence theorems

Keywords

• hammerstein equation
• branching
• bifurcation points
• asymptotics
• loads