Potential Bifurcation Theorem for a Nonhomogeneous Operator Equation and Its Application北大核心CSCD

The bifurcation phenomenon of the operator equation λ(f1'(x)+f2'(x))=g1'(x)+g2'(x) is studied in this paper. Suppose f2'≡0, f1 and g1 are a-homogeneous, and some other suitable conditions hold, Fučík et al. obtained that each normalized LS-eigenvalue of λf1'(x)=g1'(x) is a bifurcation point of the operator equation above. This paper studies the inhomogeneous case of f1+f2. We establish the same results as theirs when f1, f2, g1 and g2 satisfy some suitable conditions. A Lyusternik-Shnirel'man theorem is obtained as a preliminary result. And for the application of our abstract theorems, the bifurcation phenomenon from arbitrary LS-eigenvalues is studied for a nonlocal elliptic problem. © 2022, Chinese Academy of Sciences. All right reserved.