13 research outputs found
Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds
No full textWe consider a compact, connected, orientable, boundaryless
Riemannian manifold of class where denotes the metric tensor. Let .
Using Morse techniques, we prove the existence of
non-costant solutions to the quasilinear problem
(P_\epsilon)
\left\{ \begin{array}{l}
-\epsilon^p \, \Delta_{p,g} u +u^{p-1}=u^{q-1} \\
u>0
\end{array} \right.
\label{eqab}
for small enough, where , , and is the -laplacian associated to of
(note that ) and denotes the Poincar\'e Polynomial of .
We also establish results of genericity of nondegenerate solutions for the quasilinear elliptic problem
Morse index estimates for quasilinear equations on Riemannian manifolds
No full textThis 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))((p-2)/2)del u,) = h(x,u), where (M, g) is a compact, Riemannian manifold, 0 < alpha, 2 <= p < n. The nonlinear right-hand side h(x, s) is allowed to be subcritical or critical
Morse index estimates for quasilinear equations on Riemannian manifolds
No full textThis 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))((p-2)/2)del u,) = h(x,u), where (M, g) is a compact, Riemannian manifold, 0 < alpha, 2 <= p < n. The nonlinear right-hand side h(x, s) is allowed to be subcritical or critical
On the number of blowing-up solutions to a nonlinear elliptic equation with critical growth
No full textIn this paper we estimate the number of solutions to -Delta w + V(x)w = n(n - 2)w((n+2)/(n-2)-is an element of) in R-n w > 0 in R-n w is an element of D-1,D-2 (R-n) which blow tip at a suitable critical point of the potential V as the parameter is an element of goes to zero
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)
An Eigenvalue Problem for a Quasilinear Elliptic Field Equation on R^N
No full textWe study the field equation
on , with positive parameter.
The function is singular in a point and so the configurations are characterized
by a topological invariant: the topological charge.
By a min-max method, for sufficiently small, there
exists a finite number of solutions
of the eigenvalue problem for any given charge
Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in ℝn
No full textIn this paper, we study the nonlinear eigenvalue field equation
-Δu + V(|x|)u + ε(-Δpu + W'(u)) = μu
where u is a function from ℝn to ℝn+1 with n ≥ 3, ε is a positive parameter and p > n. We fine a multiplicity of solutions, symmetric with respect to an action of the orthogonal group O(n): For any q ∈ ℤ we prove the existence of finitely many pairs (u, μ) solutions for ε sufficiently small, where u is symmetric and has topological charge q. The multiplicity of our solutions can be as large as desired, provided that the singular point of W and ε are chosen accordingly.Mathematic
The role of taxation in an integrated economic-environmental model: a dynamical analysis
No full textWe propose a model with economic and environmental domains that interact with each other. The economic sphere is described by a Solow growth model, in which productivity is not exogenous but negatively affected by the stock of pollution that stems from the production process. A regulator can charge a tax on production, and the resources collected from taxation are used to reduce pollution. The resulting model consists of a two dimensional discrete dynamical system, and we study the role of taxation from both a static and a dynamical point of view. The focus is on the determination of the conditions under which taxation has a positive effect on the environment and leads to economic growth. Moreover, we show that a suitable environmental policy can allow recovering both local and global stability of the steady states. On the contrary, we show that, if the policy is not adequate, the system can exhibit endogenous oscillating and chaotic behavior and multistability phenomena
Displaying risk in mergers: a diagrammatic approach for exchange ratio determination
No full textThis article extends, in a stochastic setting, previous results in the
determination of feasible exchange ratios for merging companies. A first
outcome is that shareholders of the companies involved in the merging process
face both an upper and a lower bounds for acceptable exchange ratios. Secondly,
in order for the improved `bargaining region' to be intelligibly displayed, the
diagrammatic approach developed by Kulpa is exploited
