103,309 research outputs found
Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces
No full textIn this work, we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p>2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi (Boll. U.M.I. (4) 11(Suppl. fasc. 3): 1-32, 1975), using the new definition of nondegeneracy given in (Cingolani- Vannella, Ann. Inst. H. Poincaré: Analyse Non Linéaire. 20:271-292, 2003). We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini (Nonlinear Anal. T.M.A. 12:761-775, 1988) in the Hilbert case, to our Banach setting
«Audite sompnium meum». Politica e sogno in Giovanni da Legnano
No full textG. Cingolani e M. Riccini sono i curatori dell'opera.
Il saggio evidenzia le concezioni eistemologihe che sottostanno alla difesa, da parte di Giovanni da Legnano, del ruolo del sapere giuridico-canonistico nel contesto dell'Università di tardo Trecento. In particolare, gli esponenti della Facoltà delle Arti ed i teologi sono avvertiti come una minaccia da un Giovanni da Legnano, che si difende facendo sfoggio delle sue conoscenze sia filosofiche, sia teologiche
Cingolani Mario
No full textCingolani Mario: biografia e impegno educativo nell'ambito dello scautismo cattolico italiano (Asci)
Critical groups computations on a class of Sobolev Banach spaces via Morse index
No full textIn this paper we deal with critical groups estimates for a functional f:W_0^{1,p}(Ω)→R (p>2), Ω bounded domain of R^N, defined by setting f(u)=1/p∫_Ω|∇u|^p dx
+1/2∫_Ω|∇u|^2dx+∫_Ω G(u)dx where G(t)=∫_0^t g(s)ds and g is a smooth real function on R, growing subcritically. We remark that the second derivative of f in each critical point u is not a Fredholm operator from W_0^{1,p}(Ω) to its dual space, so that the generalized Morse splitting lemma does not work. In spite of the lack of a Hilbert structure, we compute the critical groups of f in u via its Morse index
Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds
No full textWe consider a compact, connected, orientable, boundaryless Riemannian manifold (M, g) of class C∞ where g denotes the metric tensor. Let n = dim M ≥ 3. Using Morse techniques, we prove the existence of nonconstant solutions u H1,p(M) to the quasilinear problem (P-epsilon) left{{egin{array}{@{}l@{}} -epsilon^p Delta-{p,g} u +u^{p-1}=u^{q-1}, \u>0,end{array}}
ight for ε > 0 small enough, where 2 ≤ p < n, p < q < p∗, p∗= np/(n - p) and is the p-laplacian associated to g of u (note that Δ2,g = Δg) and denotes the Poincaré polynomial of M. We also establish results of genericity of nondegenerate solutions for the quasilinear elliptic problem (Pε)
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