Continuation of solutions of constrained extremum problems and nonlinear eigenvalue problems

In this paper we continue our investigations, begun in the previous paper, of describing the solution sets of a constrained extremum problems inf f(u), uεt−1(p) (*) where f and t are twice continuously differentiable functionals on a reflexive Banach space V, and t-1(p) denotes the level set of the functional t with value p ε R. Considering p as a parameter in (*) we obtain results concerning the continuation of solutions of (*) and consequently also concerning specific solution branches of the nonlinear eigenvalue problem f′(u) = μt′(u) (**). The general results are applied to functionals which lead to nonlinear eigenvalue problems of a semilinear elliiptic type and in particular we cosider a specific example for which there occurs “bending” of a solution curve (u,μ) of (**).