Parameterized splitting theorems and bifurcations for potential operators

Abstract

We show that parameterized versions of splitting theorems in Morse theory can be effectively used to generalize some famous bifurcation theorems for potential operators. In particular, such generalizations based on the author's recent splitting theorems [38, 39, 42, 43] and that of [8] are given though potential operators in [42, 43] have weaker differentiability, even discontinuous. As applications, we obtain many bifurcation results for quasi-linear elliptic Euler equations and systems of higher order.

73 pages. arXiv admin note: a complete rewriting and large extension for last version

References in corpus (3)

• Delaunay-type hypersurfaces in cohomogeneity one manifolds
• Equivariant bifurcation in geometric variational problems
• Splitting lemmas for the Finsler energy functional on the space of $H^1$-curves

Cited by in corpus (2)

• Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems
• Morse theory methods for a class of quasi-linear elliptic systems of higher order