@article{
	11589_5945,
	author = { Vannella G},
	title = {Some qualitative properties of the solutions of an elliptic equation via Morse theory},
	year = {1997},
	journal = {TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS},
	volume = {9},
	pages = {297--312}
}
@article{
	11589_11619,
	author = { Vannella G},
	title = {Morse theory applied to a $T^2$-equivariant problem},
	year = {2001},
	journal = {TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS},
	volume = {17},
	keywords = {PDE; critical points; Morse theory; group actions},
	pages = {41--53}
}
@article{
	11589_5875,
	author = { Cingolani Silvia  and  Vannella G },
	title = {Some results on critical groups for a class of functionals defined on Sobolev Banach spaces},
	year = {2001},
	journal = {ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI},
	volume = {12},
	abstract = {We present
critical groups estimates for a functional f defined on the
Banach space $W_0^{1,p}(Ω)$, where Ω is a bounded domain in
R^N, p>2, associated to a quasilinear elliptic
equation involving p-laplacian. In spite of the lack of an
Hilbert structure and of Fredholm property of the second
order differential of f in each critical point, we compute the critical
groups of f in each isolated critical point via Morse index.},
	keywords = {p-laplacian; critical groups estimates; Morse index},
	pages = {199--203}
}
@conference{
	11589_16043,
	author = { Vannella G},
	title = {Critical groups estimates for a soliton type problem.},
	year = {2001},
	journal = {NONLINEAR ANALYSIS},
	volume = {47},
	booktitle = {Nonlinear Analysis: Theory, Methods & Applications. Proceedings of the Third World Congress of Nonlinear Analysts},
	abstract = {This work is concerned about applicability of Morse Theory to a class of quasilinear problems whose solutions are critical points of a functional defined on a Sobolev Banach space which has not a Hilbert structure.

The work explains what kinds of difficulties arise, shows the crucial role of critical groups and finally announces a result about the computation of such critical groups.},
	doi = {10.1016/S0362-546X(01)00694-0},	
	pages = {5999--6008}
}
@article{
	11589_11426,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {Some results on critical groups for a class of functionals defined on Sobolev Banach spaces},
	year = {2001},
	journal = {ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI},
	volume = {12},
	pages = {199--203}
}
@article{
	11589_11616,
	author = { Vannella G},
	title = {Existence and multiplicity of solutions for nonlinear Neumann problem},
	year = {2002},
	journal = {ANNALI DI MATEMATICA PURA ED APPLICATA},
	volume = {180},
	abstract = {We consider a Neumann problem of the type -εΔu+F′(u(x))=0 in an open bounded subset Ω of R^n, where F is a real function which has exactly k maximum points. Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.},
	keywords = {PDE; critical points; Morse theory},
	doi = {10.1007/s102310100020},	
	pages = {429--440}
}
@article{
	11589_2450,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {Critical groups computations on a class of Sobolev Banach spaces via Morse index},
	year = {2003},
	journal = {ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE},
	volume = {20},
	doi = {10.1016/S0294-1449(02)00011-2/FLA},	
	pages = {271--292}
}
@conference{
	11589_16843,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {Morse index computations for a class of functionals defined in Banach spaces},
	year = {2003},
	publisher = {Birkhäuser},
	address = {BASEL-BOSTON-BERLIN},
	volume = {54},
	booktitle = {Nonlinear Equations: Methods, Models and Applications. Book Series: Progress in Nonlinear Differential Equations},
	pages = {107--116}
}
@article{
	11589_11701,
	author = { CARMONA J  and  CINGOLANI S  and  VANNELLA G },
	title = {Estimates for critical groups of solutions to quasilinear elliptic systems},
	year = {2003},
	journal = {ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS},
	volume = {2003},
	pages = {1--13}
}
@article{
	11589_5876,
	author = { Cingolani Silvia  and  Vannella G },
	title = {Critical groups computations on a class of Sobolev Banach spaces via Morse index},
	year = {2003},
	journal = {ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE},
	volume = {20},
	abstract = {In 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.},
	keywords = {Morse theory; critical groups estimate; p-Laplacian},
	doi = {10.1016/S0294-1449(02)00011-2},	
	pages = {271--292}
}
@conference{
	11589_23161,
	author = { Cingolani Silvia  and  Vannella G },
	title = {Morse index computations for a class of functionals defined in Banach spaces.},
	year = {2003},
	publisher = {Birkhauser Verlag},
	address = {BASEL - BOSTON - BERLIN},
	booktitle = {Nonlinear equations: methods, models and applications},
	abstract = {In this paper we focus our attention on the estimates of critical groups for some functionals associated to a class of quasilinear equations, involving p-Laplacian.},
	keywords = {Morse Theory; quasilinear equations; critical groups; p-Laplacian},
	pages = {107--116}
}
@article{
	11589_10367,
	author = { Carmona José  and  Cingolani Silvia  and  Vannella G },
	title = {Estimates for critical groups of solutions to quasilinear elliptic systems},
	year = {2003},
	journal = {ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS},
	volume = {2003},
	abstract = {In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we
estimate the critical groups in each critical point via its Morse index.},
	keywords = {quasilinear elliptic systems; critical groups; Morse index},
	url = {http://ejde.math.txstate.edu/},
	pages = {1--13}
}
@article{
	11589_9340,
	author = { Vannella G},
	title = {Multiplicity results for two kinds of equivariant systems},
	year = {2004},
	journal = {NONLINEAR ANALYSIS},
	volume = {59},
	abstract = {Two equivariant problems of the form εΔu = ∇F(u) are considered, where F is a real function which is invariant under the action of a group G, and, using Morse theory, for each problem an arbitrarily great number of orbits ofsolutions is founded, choosing ε suitably small.
The first problem is a O(2)-equivariant system of two equations, which can be seen as a complex
Ginzburg-Landau equation, while the second one is a system of m equations which is equivariant for the action of a finite group of real orthogonal matrices m × m.},
	keywords = {critical points; Morse theory; group actions},
	doi = {10.1016/j.na.2004.07.008},	
	pages = {283--304}
}
@article{
	11589_9486,
	author = { CINGOLANI S  and  LAZZO M  and  VANNELLA G },
	title = {Multiplicity results for a quasilinear elliptic system via Morse theory},
	year = {2005},
	journal = {COMMUNICATIONS IN CONTEMPORARY MATHEMATICS},
	volume = {7},
	doi = {10.1142/S0219199705001714},	
	pages = {227--249}
}
@article{
	11589_783,
	author = { Cingolani Silvia  and  Lazzo Monica  and  Vannella G },
	title = {Multiplicity results for a quasilinear elliptic system via Morse theory},
	year = {2005},
	journal = {COMMUNICATIONS IN CONTEMPORARY MATHEMATICS},
	volume = {7},
	abstract = {In this work we prove some multiplicity results for solutions of a system of elliptic quasilinear equations, involving the p-Laplace operator (p > 2). The proofs are based on variational and topological arguments and make use of new perturbation results in Morse theory for the Banach space W_0^{1,p}.},
	keywords = {quasilinear elliptic systems; Morse theory; critical groups; degenerate critical points},
	doi = {10.1142/S0219199705001714},	
	pages = {227--249}
}
@article{
	11589_6294,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {Morse index and critical groups for p-Laplace equations with critical exponents},
	year = {2006},
	journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
	volume = {3},
	doi = {10.1007/s00009-006-0093-7},	
	pages = {495--512}
}
@article{
	11589_9118,
	author = { Cingolani Silvia  and  Vannella G },
	title = {Morse index and critical groups for p-Laplace equations with critical exponents},
	year = {2006},
	journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
	volume = {3},
	abstract = {In this work we consider a class of Euler functionals defined in Banach spaces, associated to quasilinear elliptic problems involving the critical Sobolev exponent. We perform critical groups estimates via the Morse index.},
	keywords = {p-Laplace equation; critical exponent; critical group; Morse index},
	doi = {10.1007/s00009-006-0093-7},	
	pages = {495--512}
}
@article{
	11589_785,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces},
	year = {2007},
	journal = {ANNALI DI MATEMATICA PURA ED APPLICATA},
	volume = {186},
	abstract = {In 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.},
	keywords = {p-Laplace operator; Perturbation results; Morse theory},
	doi = {10.1007/s10231-005-0176-2},	
	pages = {157--185}
}
@article{
	11589_6558,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {Multiple positive solutions for a critical quasilinear equation via Morse theory},
	year = {2009},
	journal = {ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE},
	volume = {26},
	abstract = {We deal with the existence of solutions for the quasilinear problem(P_λ) {(- Δ_p u = λ u^{q-1} + u^{p*-1}, in Ω,; 
u > 0, in Ω,; 
u = 0, on ∂ Ω,) 
where Ω is a bounded domain in R^N with smooth boundary, N≥p^2, 1<p≤q<p*, p*=Np/(N-p), λ>0 is a parameter. Using Morse techniques in a Banach setting, we prove that there exists λ* > 0 such that, for any λ ∈ (0, λ*), (P_λ) has at least P_1(Ω) solutions, possibly counted with their multiplicities, where P_t (Ω) is the Poincaré polynomial of Ω. Moreover for p ≥ 2 we prove that, for each λ ∈ (0, λ*), there exists a sequence of quasilinear problems, approximating (P_λ), each of them having at least P_1(Ω) distinct positive solutions.},
	keywords = {p-Laplace equations; critical Sobolev exponent; perturbation results; Morse theory; critical groups},
	doi = {10.1016/j.anihpc.2007.09.003},	
	pages = {397--413}
}
@article{
	11589_6423,
	author = { CINGOLANI S  and  VANNELLA G },
	title = {On the multiplicity of positive solutions for p-Laplace equations via Morse theory},
	year = {2009},
	journal = {JOURNAL OF DIFFERENTIAL EQUATIONS},
	volume = {247},
	abstract = {Let us consider the quasilinear problem(P_ε) 
{(-ε^p Δ_p u + u^{p-1} =f(u), in Ω,; 
u>0, in Ω,; 
u=0, on ∂Ω) where Ω is a bounded domain in R^N with smooth boundary, N > p, 2 ≤ p < p*, p* = Np /(N - p), ε > 0 is a parameter. We prove that there exists ε* > 0 such that, for any ε ∈]0,ε*[, (P_ε) has at least 2P_1(Ω)-1 solutions, possibly counted with their multiplicities, where P_t(Ω) is the Poincaré polynomial of Ω. Using Morse techniques, we furnish an interpretation of the multiplicity of a solution, in terms of positive distinct solutions of a quasilinear equation on Ω, approximating (P_ε).},
	keywords = {p-Laplace equations; Perturbation results; Morse theory; critical groups},
	doi = {10.1016/j.jde.2009.07.035},	
	pages = {3011--3027}
}