×

Remarks on some quasilinear elliptic equations. (English) Zbl 0325.35038


MSC:

35J60 Nonlinear elliptic equations
35P05 General topics in linear spectral theory for PDEs
35B20 Perturbations in context of PDEs
35B45 A priori estimates in context of PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Agmon, Ann. Scuola Norm. Sup. Pisa 13 pp 405– (1959)
[2] Agmon, Comm. Pure Appl. Math. 12 pp 623– (1959)
[3] Comm. Pure Appl. Math. 17 pp 35– (1964)
[4] Ambrosetti, Ann. di Mat. Pura App., IV 93 pp 231– (1972)
[5] Amann, Arch. Rat. Mech. Anal. 44 pp 178– (1972)
[6] Amann, J. Funct. Anal., V. 17 pp 174– (1974)
[7] Existence theorems, some qualitative results and a priori bounds for a class of nonlinear Dirichlet problems, to appear.
[8] and , Sur le problèeme de Dirichlet, quasilineaire, d’ordre 2, C. R. Acad, Sc., Paris, 274, Ser. A, 1972, pp. 81–85.
[9] and , Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, to appear.
[10] Dolph, Tans. Amer. Math. Soc. 66 pp 289– (1949)
[11] Fucik, Springer Lecture Notes in Math. 346 (1973) · Zbl 0268.47056 · doi:10.1007/BFb0059360
[12] Fujita, Bull. A.M.S. 75 pp 132– (1969)
[13] Joseph, Arch. Rat. Mech. Anal. 49 pp 241– (1973)
[14] Kazdan, Ann. of Math. 99 pp 14– (1974)
[15] Kazdan, J. Diff. Geo 10 pp 113– (1975)
[16] and , Positive solutions of convex nonlinear eigenvalue problems, to appear. · Zbl 0329.35028
[17] Keller, J. Math. Mech. 16 pp 1361– (1967)
[18] Klingelhofer, Arch. Rat. Mech. Anal. 37 pp 381– (1970)
[19] Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, G. B., 1964 (translated from the 1956 Russian edition).
[20] and , Linear operators which leave a cone in Banach space invariant, Amer. Math. Soc. Trans. Series 1, No. 26, 1950 (translated from Uspekhi Mat. (N.S.) 3, 1948, pp. 3–95 ). · Zbl 0030.12902
[21] and , Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech., 1970, pp. 609–623. · Zbl 0193.39203
[22] Landesman, Pacific J. of Math. 33 pp 311– (1970) · Zbl 0204.12002 · doi:10.2140/pjm.1970.33.311
[23] Mesirov, Bull. A.M.S. 80 pp 1260– (1974)
[24] Multiple Integrals in the Calculus of Variations, Grundlehren, Vol. 130, Springer-Verlag, New York, 1966.
[25] An application of generalized degree to a class of nonlinear problems, in Troisieme Colloq. Analyse Fonctionelle Liege, Sept. 1970, Centre Belge de Rech. Math., Vander, 1971.
[26] Pokhozhaev, Soviet Math. Doklady 6 pp 1408– (1965)
[27] Akad. Nauk. SSSR 165 pp 33– (1965)
[28] Pokhozhaev, Math. USSR Sbornik 11 pp 171– (1970)
[29] Russian Mat. Sbornik 82 pp 124– (1970)
[30] and , Maximum Principles in Differential Equations, Prentice-Hall, New Jersey, 1967.
[31] Rosen, J. Math. Phys. 7 pp 2066– (1966)
[32] Sattinger, Springer Lecture Notes in Math. 309 (1973) · doi:10.1007/BFb0060079
[33] Schaefer, Math. Ann. 129 pp 415– (1955)
[34] Serrin, Arch. Rat. Mech. Anal. 44 pp 182– (1972)
[35] Stampacchia, Comm. Pure Appl. Math. 16 pp 383– (1963)
[36] Rabinowitz, Indiana Univ. Math. J. 23 pp 729– (1974)
[37] On a nonlinear boundary value problem, Bull. Aust. Math. Soc., to appear.
[38] to appear.
[39] and , On the solutions of a nonlinear Dirichlet problem, to appear.
[40] The Dirichlet Problem for Nonlinear Elliptic Equations: A Hilbert Space Approach, Springer Lecture Notes No. 446, Partial Differential Equations and Related Topics, 1975, pp. 144–165.
[41] Payne, Pacific J. Math. 8 pp 551– (1958) · Zbl 0093.10901 · doi:10.2140/pjm.1958.8.551
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.