1,720,971 research outputs found
Bonheure, D. - Le Théier. Le technicien d'agriculture tropicale, 1988
No full textHuetz de Lemps Alain. Bonheure, D. - Le Théier. Le technicien d'agriculture tropicale, 1988. In: Cahiers d'outre-mer. N° 175 - 44e année, Juillet-septembre 1991. p. 313
Embedding theorems and existence results for nonlinear Schrödinger-Poisson systems with unbounded and vanishing potentials
No full textMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger-Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials. © 2011 Elsevier Inc
Multiple positive radial solutions on annuli for nonlinear Neumann problems with large growth
No full textWe consider a classical semilinear elliptic equation with Neumann boundary conditions on an annulus in RN. The nonlinear term is the product of a radially symmetric coefficient with a pure power. We prove that if the power is sufficiently large, the problem admits at least three distinct positive and radial solutions. In case the coefficient is constant, we show that none of the three solutions is constant. The methods are variational and are based on the study of a suitable limit problem. © 2010 Springer Basel AG.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
On the Born–Infeld equation for electrostatic fields with a superposition of point charges
No full textIn this paper, we study the static Born–Infeld equation -div(∇u1-|∇u|2)=∑k=1nakδxkinRN,lim|x|→∞u(x)=0,where N≥ 3 , ak∈ R for all k= 1 , ⋯ , n, xk∈ RN are the positions of the point charges, possibly non-symmetrically distributed, and δxk is the Dirac delta distribution centered at xk. For this problem, we give explicit quantitative sufficient conditions on ak and xk to guarantee that the minimizer of the energy functional associated with the problem solves the associated Euler–Lagrange equation. Furthermore, we provide a more rigorous proof of some previous results on the nature of the singularities of the minimizer at the points xk’s depending on the sign of charges ak’s. For every m∈ N, we also consider the approximated problem -∑h=1mαhΔ2hu=∑k=1nakδxkinRN,lim|x|→∞u(x)=0where the differential operator is replaced by its Taylor expansion of order 2m (see (2.1)). It is known that each of these problems has a unique solution. We study the regularity of the approximating solution, the nature of its singularities, and the asymptotic behavior of the solution and of its gradient near the singularities
Concentration on circles for nonlinear schrödinger-poisson systems with unbounded potentials vanishing at infinity
No full textThe present paper is devoted to weighted nonlinear Schrödinger-Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle. © 2012 World Scientific Publishing Company
The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate
Full text linkWe derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation
and we establish its nondegeneracy. For the corresponding three-dimensional problem, the nondegeneracy property of the positive ground state to the Choquard equation was proved by E. Lenzmann (2009)
Bifurcation analysis of the Hardy-Sobolev equation
Full text linkIn this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation [Formula presented] where N≥3, s∈[0,2), [Formula presented] and [Formula presented]. We extend results of E.N. Dancer, F. Gladiali, M. Grossi (2017) [12] where only the case s=0 is considered. The results specially rely on a careful analysis of the kernel of the linearized operator. Moreover, thanks to monotonicity properties of the solutions, we separate two branches of non-radial solutions
Classical and non-classical positive solutions of a prescribed curvature equation with singularities
Full text linkinfo:eu-repo/semantics/publishe
Symmetry of extremal functions in Moser-Trudinger inequalities and a Hénon type problem in dimension two
No full textIn this paper, we analyze the symmetry properties of maximizers of a H enon type functional in dimension two. Namely, we study the symmetry of the functions that realize the maximum:
where is the unit ball of and . We identify and study the limit functional:
which is the main ingredient to describe the behavior of maximizers as . We also consider the limit functional as and the properties of its maximizers
- …
