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Exemples d'applications holomorphes d'indice un

Rabah Souam (1993)

Annales de l'institut Fourier

Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.

Existence and density results for retarded subdifferential evolution inclusions

Tiziana Cardinali, Simona Pieri (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation theorem")....

Existence and multiplicity of solutions for a class of damped vibration problems with impulsive effects

Jianwen Zhou, Yongkun Li (2011)

Annales Polonici Mathematici

Some sufficient conditions on the existence and multiplicity of solutions for the damped vibration problems with impulsive effects ⎧ u”(t) + g(t)u’(t) + f(t,u(t)) = 0, a.e. t ∈ [0,T ⎨ u(0) = u(T) = 0 ⎩ Δ u ' ( t j ) = u ' ( t ⁺ j - u ' ( t ¯ j ) = I j ( u ( t j ) ) , j = 1,...,p, are established, where t ₀ = 0 < t ₁ < ⋯ < t p < t p + 1 = T , g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and I j : ℝ → ℝ , j = 1,...,p, are continuous. The solutions are sought by means of the Lax-Milgram theorem and some critical point theorems. Finally, two examples are presented to illustrate the effectiveness of our results....

Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

Nikolaos Papageorgiou, Francesca Papalini (2000)

Annales Polonici Mathematici

We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.

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