1,721,074 research outputs found
Metodi variazionali e topologici nello studio delle equazioni di Schrödinger nonlineari agli stati stazionari
No full textOn the multiplicity of positive solutions for p-Laplace equations via Morse theory
No full textLet 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 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)
Ground states for the pseudo-relativistic Hartree equation with external potential
No full textWe prove the existence of positive ground state solutions to the pseudo-relativistic Schrödinger equation {equation presented}, where N ≥ 3, m > 0, V is a bounded external scalar potential and W is a radially symmetric convolution potential satisfying suitable assumptions. We also provide some asymptotic decay estimates of the found solutions
Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations
No full textFor a class of nonlinear Schrodinger equations, we prove the existence of semiclassical stationary states with possibly infinitely many concentration points. As (h) over bar --> 0, these states concentrate near critical points of the potential. Furthermore, for periodic potential, these states can be constructed to satisfy periodic boundary conditions
Nonexistence of single blow-up solutions for a nonlinear Schrödinger equation involving critical Sobolev exponent
No full textMulti-peak periodic semiclassical states for a class of nonlinear Schrödinger equations
No full textMarino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces
No full textIn 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
On some qualitative aspects for doubly nonlocal equations
No full textIn this paper we investigate some qualitative properties of the solutions to the following doubly nonlocal equation
(−Δ)su+μu=(Iα∗F(u))F′(u)in RN (P)
where
N≥2
,
s∈(0,1)
,
α∈(0,N)
,
μ>0
is fixed,
(−Δ)s
denotes the fractional Laplacian and
Iα
is the Riesz potential. Here
F∈C1(R)
stands for a general nonlinearity of Berestycki-Lions type. We obtain first some regularity result for the solutions of (P). Then, by assuming
F
odd or even and positive on the half-line, we get constant sign and radial symmetry of the Pohozaev ground state solutions related to equation (P). In particular, we extend some results contained in [23]. Similar qualitative properties of the ground states are obtained in the limiting case
s=1
, generalizing some results by Moroz and Van Schaftingen in [52] when
F
is odd
Multiple S^1-orbits for the Schrodinger-Newton system
No full textWe prove existence and multiplicity of symmetric solutions for the Schrodinger-Newton system in three-dimensional space using equivariant Morse theory
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