Bifurcation points of equations involving even multi-linear functions with application to elliptical differential equations

Abstract

We consider bifurcation points of the equation where , are linear mappings; K is a nonlinear mapping of” higher order ” are functions with m an even number; and μ is a real number . Given a characteristic value of the pair (T, L0 ) such that the mapping T−L 0() is a Fredholm operator with nullity p and index zero, we prove, under additional hypotheses, that (, 0) is a bifurcation point; moreover, in general ( in some special cases ), there exist at least 2 ( 2p, respectively ) distinct parameter families of nontrivial solutions in a neighborhood of (,0)