Summary
We study radial solutions u=(u1, u2) in an exterior domain ofR N (N⩾3)of the elliptic system−Δu+V⊂u)=0, where V is a positive and singular potential. We look for solutions which satisfy Dirichlet boundary conditions and vanish at infinity. We prove existence of infinitely many radial solutions, which can be topologically classified by their winding numbers around the singularity of V. Furthermore, we study some qualitative properties of such solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V.Benci - D.Fortunato,Solitons and Relativistic Dynamics, preprint.
V. Benci -D. Fortunato -L. Pisani,Remarks on topological solitons, T.M.N.A.,7 (1996), pp. 349–367.
V.Benci - D.Fortunato - L.Pisani,Soliton like solutions of a Lorentz invariant equation in dimension 3, to appear on Reviews in Math. Phys.
H. Berestycki -P. L. Lions,Nonlinear scalar field equations, I-Existence of a ground state, Arch. Rational Mech. Anal.,82 (1983), pp. 313–375.
M. S. Berger,On the existence and structure of stationary states for a nonlinear Klein-Gordon equation, J. Funct. Anal.,9 (1972), pp. 249–261.
P. Caldiroli -L. Jeanjean,Homoclinics and heteroclinics for a class of conservative singular Hamiltonian system, J. Diff. Eq.,136 (1997), pp. 76–114.
P. Caldiroli -M. Nolasco,Multiple homoclinic solutions for a class of autonomous singular systems in R 2, Ann. Inst. H. Poincaré, Anal. Nonlin.,15 (1998), pp. 113–125.
G. Citti,Positive solutions for a quasilinear degenerate elliptic equation in R N, Rend. Circ. Mat. Palermo, s. 2,XXXV (1986), pp. 364–375.
R. K. Dodd -J. C. Eilbeck -J. D. Gibbon -H. C. Morris,Solitons and nonlinear wave equations, Academic Press, London, New York (1982).
W. Gordon,Conservative dynamical systems involving strong forces, Trans. A.M.S.,204 (1975), pp. 113–135.
S. Lang,Complex Analysis, Springer-Verlag, Heidelberg (1993).
J. L. Lions,Problèmes aux limites dans les équations aux dérivées partielles, Presses de l'Univ. de Montréal, Montréal (1962).
P.Rabinowitz,Homoclinic for a singular Hamiltonian system, Geometric Analysis and the Calculus of variations (J. Jost ed.), International Press, to appear.
W. A. Strauss,Existence of solitary waves in higher dimensions, Comm. Math. Phys.,55 (1977), pp. 149–162.
Author information
Authors and Affiliations
Additional information
Supported by M.U.R.S.T. (40% and 60% funds) and E.E.C., Program Human Capital Mobility (Contract ERBCHRXCT 940494).
Rights and permissions
About this article
Cite this article
Cingolani, S., Lazzo, M. & Padial, J.F. Multiple radial solutions for a class of elliptic systems with singular nonlinearities. Annali di Matematica pura ed applicata 175, 365–373 (1998). https://doi.org/10.1007/BF01783693
Issue Date:
DOI: https://doi.org/10.1007/BF01783693