Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds

Journal article

Peer reviewed

S Cingolani, G Vannella and Daniela Visetti

Communications in Contemporary Mathematics, Vol.17(2)

17

2015

Handle:

https://hdl.handle.net/10863/3441

Abstract

Perturbation results

Morse index

Quasilinear elliptic equations

Positive solutions

Riemannian manifold

url

http://www.worldscientific.com/doi/abs/10.1142/S0219199714500291View

Title: Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds
Creators: S Cingolani
G Vannella
Daniela Visetti
Publication Details: Communications in Contemporary Mathematics, Vol.17(2)
ISSN: 0219-1997
Series / Volume: 17
Publisher: World Scientific Publishing Co. Pte Ltd
Number of pages: 41
Identifiers: (UNIBZ)23302598
991005773641801241
Web of Science ID: 000351756100008
Scopus ID: 2-s2.0-84928473477
Academic Unit: Faculty of Economics and Management
Language: English
Resource Type: Journal article
Author Names String: Cingolani S, Vannella G, Visetti D
Additional Description: description: We consider a compact, connected, orientable, boundaryless Riemannian manifold (M, g) of class C-infinity where g denotes the metric tensor. Let n = dim M >= 3. Using Morse techniques, we prove the existence of 2P(1)(M) - 1 nonconstant solutions u is an element of H-1,H- p (M) to the quasilinear problem (P-is an element of) {-(p) Delta(p,g) u + u(p-1) = u(q-1), u > 0, for epsilon > 0 small enough, where 2 <= p < n, p < q < p*, p* = np/(n - p) and Delta(p, g) u = div(g) (vertical bar del u vertical bar(p-2)(g) del u) is the p-laplacian associated to g of u (note that Delta(2, g) = Delta(g)) and P-t(M) denotes the Poincare polynomial of M. We also establish results of genericity of nondegenerate solutions for the quasilinear elliptic problem (P-epsilon).

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