Geodesic
On the solution of Hammerstein integral equations with loads and bifurcation parameters
The Bulletin of Irkutsk State University. Series Mathematics, Tome 43 (2023), pp. 78-90

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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, asymptotics, loads.
Mots-clés : bifurcation points 
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     author = {N. A. Sidorov and Lev Ryan D. Dreglea Sidorov},
     title = {On the solution of {Hammerstein} integral equations with loads and bifurcation parameters},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a5/}
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N. A. Sidorov; Lev Ryan D. Dreglea Sidorov. On the solution of Hammerstein integral equations with loads and bifurcation parameters. The Bulletin of Irkutsk State University. Series Mathematics, Tome 43 (2023), pp. 78-90. http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a5/