Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds
Subject
Riemannian manifold; Positive solutions; Quasilinear elliptic equations; Morse index; Perturbation resultsAbstract
We consider a compact, connected, orientable, boundaryless Riemannian manifold (M, g) of class Cinfinity 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 H1,H p (M) to the quasilinear problem
(Pis an element of) {(p) Delta(p,g) u + u(p1) = u(q1), 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(p2)(g) del u) is the plaplacian associated to g of u (note that Delta(2, g) = Delta(g)) and Pt(M) denotes the Poincare polynomial of M. We also establish results of genericity of nondegenerate solutions for the quasilinear elliptic problem (Pepsilon).
URI
http://dx.doi.org/10.1142/S0219199714500291http://www.worldscientific.com/doi/abs/10.1142/S0219199714500291
http://hdl.handle.net/10863/3441
Collections
Related items
Showing items related by title, author, creator and subject.

Morse index estimates for quasilinear equations on Riemannian manifolds
Cingolani S; Vannella G; Visetti D (2011)This work deals with Morse index estimates for a solution u is an element of H(1)(p)(M) of the quasilinear elliptic equation div(g) ((alpha + del u(2)(g))((p2)/2)del u,) = h(x,u), where (M, g) is a compact, Riemannian ... 
An eigenvalue problem for a quasilinear elliptic field equation
Visetti D (Elsevier, 2001)We study the field equation Deltau + V(x)u + epsilon (Delta (p)u + W'(u)) = mu mu on a bounded domain and on Rn, with E positive parameter. The function W is singular in a point and so the configurations are characterized ... 
An eigenvalue problem for a quasilinear elliptic field equation on R^n
Benci V; Micheletti A; Visetti D (2001)We study the field equation −Δu+V(x)u+εr(−Δpu+W′(u))=μu on Rn, with ε positive parameter. The function W is singular in a point and so the configurations are characterized by a topological invariant: the topological ...