UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR
Xiaofei CAO1, Guowei DAI2
1. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China; 2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
[1] Chen A, Li R. Characterizations of some matirx classes of quasi-homogeneous operators. Acta Math Sci, 2012, 32B(6):2285-2294 [2] Dai G. Two global several-parameter bifurcation theorems and their applications. J Math Anal Appl, 2016, 433:749-761 [3] Dambrosio W. Global bifurcation from the Fučik spectrum. Rend Semin Mat Univ Padova, 2000, 103:261-281 [4] Dancer E N. On the structure of solutions of non-linear eigenvalue problems. Indiana Univ Math J, 1974, 23:1069-1076 [5] Dancer E N. Bifurcation from simple eigenvalues and eigenvalues of geometric multiplicity one. Bull London Math Soc, 2002, 34:533-538 [6] Drábek P. Solvability and Bifurcations of Nonlinear Equations, in Pitman Research Notes in Mathematics. Harlow/New York:Longman, 1992 [7] Fizpztrick P M, Massabò I, Pejsachowicz J. Global several-parameter bifurcation and continuation theorems:a unified approch via completmenting maps. Math Ann, 1983, 263:61-73 [8] Krasnosel'skii M A. Topological Methods in the Theory of Nonlinear Integral Equations. New York:Macmillan, 1965 [9] López-Gómez J. Spectral Theory and Nonlinear Functional Analysis. Boca Raton:Chapman and Hall/CRC, 2001 [10] Rabinowitz P H. Some global results for nonlinear eigenvalue problems. J Funct Anal, 1971, 7:487-513 [11] Schwartz J T. Nonlinear Functional Analysis. New York:Gordon and Breach, 1969