Quasilinear Dirichlet problems driven by positive sources. (English) Zbl 0266.34021


34B15 Nonlinear boundary value problems for ordinary differential equations
41A15 Spline approximation
34C99 Qualitative theory for ordinary differential equations
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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[1] Joseph, D. D., Non-linear heat generation and the stability of the temperature distribution in conducting solids. Int. J. Heat Mass Transfer 8, 281–288 (1965). · Zbl 0127.05006
[2] Keller, H., & D. Cohen, Some positone problems suggested by nonlinear heat generation. J. Math. Mech. 16, 1361–1376 (1967). · Zbl 0152.10401
[3] Joseph, D. D., & E. M. Sparrow, Nonlinear diffusion induced by nonlinear sources. Quart. Appl. Math. 28, 327–342 (1970). · Zbl 0208.13006
[4] Gelfand, I. M., Some problems in the theory of quasilinear equations. Amer. Math. Soc. Transl. (2) 29, 295–381 (1963).
[5] Callegari, A. J., E. L. Reiss, & H. Keller, Membrane buckling. Comm. Pure Appl. Math. 24, 499–527 (1971). · Zbl 0218.73061
[6] Emden, V. R., Gaskugeln, 1907.
[7] Fowler, R. H., Further studies of Emden’s and similar differential equations. Quart. J. Math. (Oxford series) 2, 259–288 (1931). · Zbl 0003.23502
[8] Chandrasekhar, S., An Introduction to the Study of Stellar Structure New York: Dover 1957. · Zbl 0079.23901
[9] Hopf, E., On Emden’s differential equation. M.N.R.A.S. 91, 653–663 (1931). · Zbl 0002.10301
[10] Joseph, D. D., Bounds on {\(\lambda\)} for positive solutions of {\(\Delta\)}{\(\psi\)}+{\(\lambda\)}f(r)({\(\psi\)}+G({\(\psi\)}))=0. Q. Appl. Math. 23, 349–354 (1966). · Zbl 0134.31303
[11] Cole, J. D., Perturbation Methods in Applied Mathematics. Blaisdell Publishing Co. 1968. · Zbl 0162.12602
[12] Bendixson, I., Sur les courbes définies par des équations différentiells. Acta. Math. 24, 1–88 (1901).
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