Spatially heteroclinic solutions for a semilinear elliptic P.D.E.
This paper uses minimization methods and renormalized functionals to find spatially heteroclinic solutions for some classes of semilinear elliptic partial differential equations
This paper uses minimization methods and renormalized functionals to find spatially heteroclinic solutions for some classes of semilinear elliptic partial differential equations
This paper uses minimization methods and renormalized functionals to find spatially heteroclinic solutions for some classes of semilinear elliptic partial differential equations
∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria.The definition of the weak slope of continuous functions introduced by Degiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness” of locally Lipschitz functions are discussed. A deformation lemma and a mountain pass theorem for usco mappings are proved....
La caustique d?un point sur une variété riemannienne est l?ensemble des points d?intersection des géodésiques infiniment voisins partant de ce point. Jacobi a remarqué, en utilisant un raisonnement topologique, que la caustique d?un point sur une surface convexe fermée doit avoir des points de rebroussement. Il a aussi annoncé (sans démonstration) que le nombre de ces points est quatre pour les caustiques sur les surfaces d?ellipsoïdes (Jacobi, 1964). Dans cette note j?essaie d?inclure les théorèmes...
We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having...
Let be a compact CR manifold of dimension with a contact form , and its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form on conformal to which has a constant Webster curvature. This problem is equivalent to the existence of a function such that , on . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where and is not locally CR equivalent to the sphere of . In a join work with R. Yacoub, the CR Yamabe problem...