On the solution of Hammerstein integral equations with loads and bifurcation parameters. (Russian. English summary) Zbl 1512.45004
Summary: 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
MSC:
| 45G10 | Other nonlinear integral equations |
| 45L05 | Theoretical approximation of solutions to integral equations |
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