zbMATH — the first resource for mathematics

Existence of multiple positive solutions for nonlinear \(m\)-point boundary value problems. (English) Zbl 1030.34026
Summary: Here, we afford some sufficient conditions to guarantee the existence of multiple positive solutions to the nonlinear \(m\)-point boundary value problem for the one-dimensional \(p\)-Laplacian \[ \bigl( \varphi_p (u')\bigr)'+ a(t)f(t,u)=0,\;t\in(0,1), \quad u(0)=0,\;u(1)=\sum^{m-2}_{i=1} a_iu(\xi_i). \]

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
Full Text: DOI
[1] Basdevant, C.; Legras, B.; Sadourny, R.; BĂ©land, M., A study of barotropic model flows: intermittency, waves, and predictability, J. atmos. sci., 38, 2305-2326, (1981)
[2] Browning, G.L.; Kreiss, H.-O., Comparison of numerical methods for the calculation of two-dimensional turbulence, Math. comp., 52, 369-388, (1989) · Zbl 0678.76048
[3] Cannone, M., Ondelettes, paraproduits, et navier – stokes, (1995), Paris · Zbl 1049.35517
[4] Cannone, M.; Meyer, Y., Littlewood – paley decomposition and the navier – stokes equations, Methods appl. anal., 2, 307-319, (1995) · Zbl 0842.35074
[5] Cannone, M.; Planchon, F., Self-similar solutions of navier – stokes equations in \(R\^{}\{3\}\), Comm. partial differential equations, 21, 179-193, (1996) · Zbl 0842.35075
[6] Fornberg, B., A numerical study of two-dimensional turbulence, J. comput. phys., 25, 1-31, (1977) · Zbl 0461.76040
[7] Frazier, M.; Jawerth, B.; Weiss, G., Littlewood – paley theory and the study of function spaces, CBM-AMS regional conference series in mathematics, 79, (1991), American Mathematical Society
[8] Kato, T., Strong Lp-solutions to the navier – stokes equation in \(R\^{}\{m\}\), with applications to weak solutions, Math. Z., 187, 471-480, (1984) · Zbl 0545.35073
[9] Kato, T.; Fujita, H., On the non-stationary navier – stokes system, Rend. sem. mat. univ. Padova, 32, 243-260, (1962) · Zbl 0114.05002
[10] McWilliams, J.C., The emergence of isolated coherent vortices in turbulent flows, J. fluid mech., 146, 21-43, (1984) · Zbl 0561.76059
[11] Pazy, A., Semigroups of linear operators and applications to partial differential equations, (1983), Springer-Verlag New York · Zbl 0516.47023
[12] Smart, D.R., Fixed point theorems, (1974), Cambridge University Press Cambridge · Zbl 0297.47042
[13] Stein, E.M.; Weiss, G., Introduction to Fourier analysis on Euclidean spaces, (1971), Princeton University Press Princeton, NJ
[14] S. Tourville, An analysis of a numerical method for solving the two-dimensional Navier-Stokes equations, Ph.D. thesis, Washington University, St. Louis, MO (1997)
[15] Tourville, S., Existence and uniqueness of solutions for a modified navier – stokes equation in \(R\^{}\{2\}\), Comm. partial differential equations, 23, 97-121, (1998) · Zbl 0893.35093
[16] Wheeden, R.; Zygmund, A., Measure and integral, (1977), Dekker New York
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.