Cazenave, Thierry Equations de Schrödinger non linéaires en dimension deux. (French) Zbl 0428.35021 Proc. R. Soc. Edinb., Sect. A 84, 327-346 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 30 Documents MSC: 35J10 Schrödinger operator, Schrödinger equation 35Q99 Partial differential equations of mathematical physics and other areas of application 35J60 Nonlinear elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B65 Smoothness and regularity of solutions to PDEs 35D10 Regularity of generalized solutions of PDE (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs 78A05 Geometric optics 78A10 Physical optics 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:nonlinear perturbations; Schrödinger equation; nonlinear optics; existence, uniqueness and regularity of solutions; Cauchy problem; asymptotic behaviour of the solutions; rates of decay PDFBibTeX XMLCite \textit{T. Cazenave}, Proc. R. Soc. Edinb., Sect. A, Math. 84, 327--346 (1979; Zbl 0428.35021) Full Text: DOI References: [1] Baillon, C. R. Acad. Sci. Paris Sér. A-B 284 pp 939– (1977) [2] Baillon, C.R. Acad. Sci. Paris Sér. A-B 284 pp 869– (1977) [3] Aitken, N.R.L. Report 7293 (1971) [4] Suydam, Spec. Publs Natn. Bur. Stand. 387 pp 42– (1973) [5] DOI: 10.1016/S0304-0208(08)70877-6 [6] Strauss, Non linear invariant wave equations [7] Berestycki, C. R. Acad. Sci. Paris Sér. A-B 287 pp 503– (1978) [8] Reed, Methods of Modern Mathematical Physics II (1975) [9] DOI: 10.1063/1.861679 [10] Nirenberg, Ann. Scuola Norm. Sup. Pisa 13 pp 115– (1959) [11] DOI: 10.1103/PhysRevLett.15.1005 [12] DOI: 10.1016/0022-1236(79)90076-4 · Zbl 0396.35028 [13] DOI: 10.2307/1970347 · Zbl 0204.16004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.