An Inclusion Theorem

Three solutions for a perturbed Dirichlet problem

Abstract In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem: { − Δ u = f ( x , u ) + λ g ( x , u ) in  Ω u = 0 on  ∂ Ω , where Ω ⊂ R N is an open bounded set with smooth boundary ∂ Ω and λ ∈ R . Under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and + ∞ , our result assures the existence of at least three distinct solutions to the above problem for λ small enough. Moreover such solutions belong to a ball of the space W 0 1 , 2 ( Ω ) centered in the origin and with radius not dependent on λ .

AN APPLICATION OF A FIXED POINT THEOREM FOR NONEXPANSIVE OPERATORS

Abstract. In this note, we present an application of a recent xed point theorem by Ricceri to a two-point boundary value problem. KeyWords and Phrases: Fixed point, nonexpansive operator, two-point boundary value problem. 2010 Mathematics Subject Classi cation: 34K10, 47H09, 47H10.

Three periodic solutions for perturbed second order Hamiltonian systems

AbstractIn this paper we study the existence of three distinct solutions for the following problem−u¨+A(t)u=∇F(t,u)+λ∇G(t,u)a.e. in [0,T],u(T)−u(0)=u˙(T)−u˙(0)=0, where λ∈R, T is a real positive number, A:[0,T]→RN×N is a continuous map from the interval [0,T] to the set of N-order symmetric matrices. We propose sufficient conditions only on the potential F. More precisely, we assume that G satisfies only a usual growth condition which allows us to use a variational approach.

Three solutions for pertubed Dirichilet problem

\begin{abstract} In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem \begin{displaymath} \left\{ \begin{array}{ll} -\Delta u= f(x,u)+\lambda g(x,u) & \mbox{in\ } \Omega\\ u=0 & \mbox{on\ } \partial \Omega, \end{array}\right. \end{displaymath} where $\Omega\subset\mathbb{R}^N$ is an open bounded set with smooth boundary $\partial \Omega$ and $\lambda\in \mathbb{R}$. Under very mild conditions on $g$ and some assumptions on the behaviour of the potential of $f$ at $0$ and $+\infty$, our result assures the existence of at least three distinct solutions to the above problem for $\lambda$ small enough. Moreover such solutions bel…

AN OPTIMIZATION THEOREM IN SPACES ADMITTING A CONTINUOUS BIJECTION ONTO [0,1]

Sulla K-variazione Essenziale di Una Funzione reale

In this paper we consider a definition of essentialK-variation for real functions which gives information on the absolute integrability of its approximate derivate on a measurable set.

SOME EXAMPLES RELATED TO A CLASS OF FUNCTIONALS WITHOUT GLOBAL MINIMA

Abstract: In this paper, we provide six examples which show the sharpness of the assumptions of a recent deep result of Ricceri about a class of functionals without global minima.

Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities