Abstract
In this paper we consider the question of minimizing functionals defined by improper integrals. Our approach is alternative to the method of concentration-compactness and it does not require the verification of strict subaddivity.
Similar content being viewed by others
References
Pohozaev, S.I., Eigenfunctions of the equation Δu+λf(u)=0. Sov. Math. Doklady 5, 1408–1411 (1965).
Strauss, W.A., Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55, 149–162 (1977).
Lions, P.L., The Concentration—Compactness Principle in the Calculus of Variations. Ann. Inst. H. Poincaré, Anal. Non Linéare, sec A, 1 (1984), Part I 109–145, Part II 223–283.
Berestycki, H. and Lions, P.L., Nonlinear Scalar Fields Equations, Part I, Arch. Rat. Mech. Analysis 82, 1983, no 4, 313–345.
Berestycki, H., Gallouet, Th., Kavian, O., Equation des Champs Scalaires Euclidiens Nonlineaires dans le Plan, C.R. Ac. Sci. Paris, serie I, Maths, 297 (1983), no 5, 307–310.
Coleman, S., Glazer, V. and A. Martin, Action minima among solutions to a class of Euclidean scalar field equations; Comm. Math Phys 58(2), 211–221 (1978).
Cazenave, T., Lions, P.L., Orbital Stability of Standing Waves for Some Nonlinear Schrödinger Equations. Comm. Math. Phys. 85, 549–561 (1982).
Brezis, H., Lieb, E.H., Minimum Action Solutions of Some Vector Field Equations, Comm. Math. Physics, 96 (1984), no 1, 97–113.
Gidas, B., Ni, W.N., and Nirenberg, L., Symmetry and Related Properties via the Maximum Principle, Comm. Math. Phys., 68 (1979), 209–243.
Lieb, E.H., On the Lowest Eigenvalue of the Laplacian for the Intersection of Two Domains, Invent. Math., 74 (1983), no 3, 441–448.
Lions, P.L., Solutions of Hartree—Fock Equations for Coulomb Systems, Comm. Math. Phys., 109, 33–97 (1987).
Kato, T. Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966.
Author information
Authors and Affiliations
Additional information
Dedicated to the memory of Antonio Gilioli (1945–1989)
About this article
Cite this article
Lopes, O. A constrained minimization problem with integrals on the entire space. Bol. Soc. Bras. Mat 25, 77–92 (1994). https://doi.org/10.1007/BF01232936
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01232936