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- Title
Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds.
- Authors
Cingolani, Silvia; Vannella, Giuseppina; Visetti, Daniela
- Abstract
We consider a compact, connected, orientable, boundaryless Riemannian manifold (M, g) of class C∞ where g denotes the metric tensor. Let n = M ≥ 3. Using Morse techniques, we prove the existence of nonconstant solutions u ∈ H1,p(M) to the quasilinear problem 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).
- Subjects
MULTIPLICITY (Mathematics); NON-degenerate perturbation theory; QUASILINEARIZATION; RIEMANNIAN manifolds; PROBLEM solving
- Publication
Communications in Contemporary Mathematics, 2015, Vol 17, Issue 2, p-1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199714500291