Sur certains problèmes elliptiques asymétriques avec poids indéfinis

Asymmetric elliptic problems with indefinite weights

“…The main results of this paper were announced in [9]. The authors wish to express their gratitude for the referee's careful and detailed comments.…”

Multiplicity Results for Asymptotically Linear Equations, Using the Rotation Number Approach

“…In her work [49], existence and multiplicity of 2π−periodic solutions for a class of asymptotically linear second order equations are achieved under assumptions involving weighted eigenvalues. Finally, and before introducing our main result, we quote the contributions provided by Arias-Campos-Cuesta-Gossez in [3] and by Rynne in [45]. Both these works deal with asymmetric problems, where a suitable asymmetric eigenvalue problem, characterized by the presence of two weights, is considered.…”

“…Both these works deal with asymmetric problems, where a suitable asymmetric eigenvalue problem, characterized by the presence of two weights, is considered. In particular, in [3] an existence result for the Dirichlet BVP associated to −∆ p u = f (t, u), whenever p > 1, is achieved under asymmetric, asymptotically 130 F. Dalbono and F. Zanolin Mediterr. j. math.…”

“…In [3], hypotheses involving the first eigenvalues are considered. For more specific information on the multiplicity results attained by Rynne in [45] we refer to the final part of the present article.…”

Bifurcations for a problem with jumping nonlinearities

“…then there is a global bifurcation of nontrivial solutions to (BP) between λ (1) and λ (2) under some assumptions about the supports of the functions α, β. These assumptions will be given by the character of the eigenfunctions of (EP) corresponding to λ (1) , λ (2) . Notice that it will be essential that α and β have supports in disjoint regions.…”