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Bibliography
S. Agmon, A. Douglis and L. Nirenberg: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions; Comm. Pure and Applied Math. 12 (1959) p. 623–727 Part. I.
A. Ambrosetti and P.H. Rabinowitz: Dual variational methods in critical point theory and applications; J. Funct. Anal. 14 (n°4) (1973) p. 349–381. Cf. also P.H. Rabinowitz: Variational methods for non-linear eigenvalue problems in Eigenvalues of non-linear problems, C.I.M.E. lecture notes, Ed. Cremonese, Roma 1974.
D.G. Aronson and L.A. Peletier: Large time behaviour of solutions of the porous media equation. To appear.
H. Berestycki et P.L. Lions: Existence d'ondes solitaires dans des problèmes non-linéaires du type Klein-Gordon. C.R.A.S. Paris-Ser. A. 287 (1978) p.503–506.
H. Berestycki and P.L. Lions: Existence of a ground state in non linear equations of the type Klein-Gordon. To appear in Variational Inequalities Ed. Gianessi, Cottle, Lions, J. Wiley, New-York.
H. Berestycki and P.L. Lions: A local approach to the existence of solitary waves for nonlinear Klein-Gordon equations.
H. Berestycki and P.L. Lions: Existence of solitary waves in non linear Klein-Gordon equations. Part I: The ground state. Part II: Existence of infinitely many bound states. To appear.
H. Berestycki and P.L. Lions: Existence d'ondes solitaires dans des problèmes non linéaires du type Klein-Gordon. C.R.A.S. Paris 288 (1979) p. 395–398.
C.M. Brauner and B. Nicolaenko: See their contribution in this volume.
H. Brézis and P.L. Lions: To appear in Bull. U.M.I.
A.M. Il'in, A.S. Kalashnikov and O.A. Oleinik: Linear equations of the second order of parabolic type. Russian Math. Surveys 17 (1962) n°3, p. 1. — 143.
N.V. Krylov: Control of a solution of a stochastic integral equation. th. Proba. Appl. Vol. XVII. n°1 (1972), p. 114–131.
P.L. Lions: Contrôle de diffusions dans IRn. To appear.
P.L. Lions: Problèmes elliptiques du 2ème ordre non sous forme divergences. To appear in Proc. Roy. Sec. Edim.
P.L. Lions and J.L. Menaldi: Control of stochastic equations and Bellman equations. To appear. See also: Problèmes de Bellman avec le contrôle dans les coefficients de plus haut degré. C.R.A.S. Paris série A, 287, (1978), p. 409–412.
S.I. Pohozaev: Eigen functions of the equation Δu+Λf(u)=0. sov. Math. Pokl. S (1965) p. 1408–1411.
P.H. Rabinowitz: Pairs of positive solutions of non linear elliptic partial differential equations, Indiana Univ. Math. J. 23 (1973/74), p. p. 173–186.
A.F. Rañada. and L. Vásquez: Kinks and the Heisenberg un certainty principle. To appear in Phys. Rev. D.
W.A. Strauss: Existence of solitary wares on higher dimensions. Comm. Math. Phys. 55 (1977), p. 149–162.
D.W. Stroock and S.R.S. Varadhan: On degenerate elliptic-parabolic operators of second order and their associated diffusions. Comm. Pure Appl. Maths. 25 (1972), p. 651–713.
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Berestycki, H., Lions, P.L. (1980). Some applications of the method of super and subsolutions. In: Bardos, C., Lasry, J.M., Schatzman, M. (eds) Bifurcation and Nonlinear Eigenvalue Problems. Lecture Notes in Mathematics, vol 782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090426
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DOI: https://doi.org/10.1007/BFb0090426
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