@article{10902/37974,
year = {2024},
url = {https://hdl.handle.net/10902/37974},
abstract = {This paper consists of four parts. It begins by using the authors' generalized Schauder formula, [41], and the algebraic multiplicity, X, of Esquinas and López-Gómez [15,14,31] to package and sharpening all existing results in local and global bifurcation theory for Fredholm operators through the recent author's axiomatization of the Fitzpatrick-Pejsachowicz-Rabier degree, [42]. This facilitates reformulating and refining all existing results in a compact and unifying way. Then, the local structure of the solution set of analytic nonlinearities F(Y,u)=0 at a simple degenerate eigenvalue is ascertained by means of some concepts and devices of Algebraic Geometry and Galois Theory, which establishes a bisociation between Bifurcation Theory and Algebraic Geometry. Finally, the unilateral theorems of [31,33], as well as the refinement of Shi and Wang [53], are substantially generalized. This paper also analyzes two important examples to illustrate and discuss the relevance of the abstract theory. The second one studies the regular positive solutions of a multidimensional quasilinear boundary value problem of mixed type related to the mean curvature operator.},
organization = {The authors have been supported by the Research Grant PID2021–123343NB-I00 of the Spanish Ministry of Science and Innovation and by the Institute of Interdisciplinar Mathematics of Complutense University.},
publisher = {Elsevier},
publisher = {Journal of Differential Equations, 2024, 404, 182-250},
title = {Bifurcation theory for Fredholm operators},
author = {López Gómez, Julián and Sampedro Pascual, Juan Carlos},
}