Effective multiplicity for the Einstein-scalar field Lichnerowicz equation

Allen, P.T., Clausen, A., Isenberg, J.: Near-constant mean curvature solutions of the Einstein constraint equations with non-negative Yamabe metrics. Classic. Quant. Grav. 25(7), 075009 (2008)

Aubin, T.: Nonlinear analysis on manifolds. Monge-Ampère equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol 252. Springer, New York (1982)

Bartnik, R., Isenberg, J.: The constraint equations. In: The Einstein Equations and the Large Scale Behavior of Gravitational Fields, pp. 1–38. Birkhäuser, Basel (2004)

Beig, R., Chruściel, P.T., Schoen, R.: Kids are non-generic. Ann. Henri Poincaré 6(1), 155–194 (2005)

Caffarelli, L.A., Gidas, B., Spruck, J.: Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth. Commun. Pure Appl. Math. 42(3), 271–297 (1989)

Choquet-Bruhat, Y., Isenberg, J., Pollack, D.: Applications of theorems of jean leray to the einstein-scalar field equations. J. Fixed Point Theory Appl. 1(1), 31–46 (2007)

Choquet-Bruhat, Y., Isenberg, J., Pollack, D.: The constraint equations for the einstein-scalar field system on compact manifolds. Classic. Quant. Grav. 24(4), 809–828 (2007)

Dahl, M., Gicquaud, R., Humbert, E.: A limit equation associated to the solvability of the vacuum einstein constraint equations by using the conformal method. Duke Math. J. 161(14), 2669–2697 (2012)

Druet, O.: Compactness for yamabe metrics in low dimensions. Int. Math. Res. Notices 23, 1143–1191 (2004)

Druet, O., Hebey, E.: Stability and instability for einstein-scalar field lichnerowicz equations on compact riemannian manifolds. Math. Z. 263(1), 33–67 (2009)

Fourès-Bruhat, Y.: Théorème d’existence pour certains systèmes d’équations aux dérivées partielles non linéaires. Acta Math. 88, 141–225 (1952)

Hebey, E., Pacard, F., Pollack, D.: A variational analysis of einstein-scalar field lichnerowicz equations on compact riemannian manifolds. Commun. Math. Phys. 278(1), 117–132 (2008)

Hebey, E., Veronelli, G.: The lichnerowicz equation in the closed case of the Einstein–Maxwell theory. Trans. Am. Math. Soc. (2011, accepted for publication)

Holst, M., Nagy, G., Tsogtgerel, G.: Rough solutions of the einstein constraints on closed manifolds without near-cmc conditions. Commun. Math. Phys. 288(2), 547–613 (2009)

Isenberg, J.: Constant mean curvature solutions of the einstein constraint equations on closed manifolds. Classic. Quant. Grav. 12(9), 2249–2274 (1995)

Li, Y., Zhu, M.: Yamabe type equations on three-dimensional riemannian manifolds. Commun. Contemp. Math. 1(1), 1–50 (1999)

Lichnerowicz, A.: L’intégration des équations de la gravitation relativiste et le problème des $$n$$ n corps. J. Math. Pures Appl. 9(23), 37–63 (1944)

Ma, L., Wei, J.: Stability and multiple solutions to Einstein-scalar field Lichnerowicz equation on manifolds. J. Math. Pures Appl. (2012). doi: 10.1016/j.matpur.2012.06.009

Maxwell, D.: A class of solutions of the vacuum einstein constraint equations with freely specified mean curvature. Math. Res. Lett. 16(4), 627–645 (2009)

Ngô, Q.A., Xu, X.: Existence results for the einstein-scalar field lichnerowicz equations on compact riemannian manifolds. Adv. Math. 230(4–6), 2378–2415 (2012)

Premoselli, B.: The Einstein-scalar field constraint system in the positive case. Commun. Math. Phys. 326(2), 543–557 (2014). doi: 10.1007/s00220-013-1852-5

Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, vol. 65. Published for the Conference Board of the Mathematical Sciences, Washington, DC (1986)

Robert, F.: Existence et asymptotiques optimales des fonctions de green des opérateurs elliptiques d’ordre deux (2009, personal notes)

Sattinger, D.H. Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J. 21, 979–1000 (1971/1972)

Schoen, R.M.: Lecture notes from courses at stanford (1988, preprint, written by D. Pollack)

Schoen, R.M.: On the number of constant scalar curvature metrics in a conformal class. In: Differential geometry, Pitman Monogr. Surveys Pure Appl. Math., vol 52, pp. 311–320. Longman Sci. Tech., Harlow (1991)

Struwe, M.: Variational methods, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 34. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], Applications to nonlinear partial differential equations and Hamiltonian systems, 4th edn. Springer, Berlin (2008)