×

zbMATH — the first resource for mathematics

Positive solutions of a nonlinear \(m\)-point boundary value problem. (English) Zbl 0987.34018
The existence of at least one positive solution is proved to a multipoint boundary value problem associated to second-order ordinary differential equations. The involved nonlinearity is assumed to be either superlinear or sublinear. A Krasnosel’skij-type fixed-point theorem is applied for this aim.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Il’in, V.A.; Moiseev, E.I., Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differential equations, 23, 7, 803-810, (1987) · Zbl 0668.34025
[2] Il’in, V.A.; Moiseev, E.I., Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator, Differential equations, 23, 8, 979-987, (1987) · Zbl 0668.34024
[3] Gupta, C.P., Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, J. math. anal. appl., 168, 540-551, (1992) · Zbl 0763.34009
[4] Feng, W.; Webb, J.R.L., Solvability of a three-point boundary value problems at resonance, Nonlinear analysis TMA, 30, 6, 3227-3238, (1997) · Zbl 0891.34019
[5] Feng, W.; Webb, J.R.L., Solvability of a m-point boundary value problems with nonlinear growth, J. math. anal. appl., 212, 467-480, (1997) · Zbl 0883.34020
[6] Feng, W., On a m-point nonlinear boundary value problem, Nonlinear analysis TMA, 30, 6, 5369-5374, (1997) · Zbl 0895.34014
[7] Gupta, C.P.; Ntouyas, S.K.; Tsamatos, P.Ch., On an m-point boundary value problem for second order ordinary differential equations, Nonlinear analysis TMA, 23, 11, 1427-1436, (1994) · Zbl 0815.34012
[8] Gupta, C.; Trofimchuk, S., Existence of a solution to a three-point boundary values problem and the spectral radius of a related linear operator, Nonlinear analysis TMA, 34, 498-507, (1998) · Zbl 0944.34009
[9] Marano, S.A., A remark on a second order three-point boundary value problem, J. math. anal. appl., 183, 581-582, (1994)
[10] Ma, R., Existence theorems for a second order three-point boundary value problem, J. math. anal. appl., 212, 430-442, (1997) · Zbl 0879.34025
[11] Ma, R., Positive solutions of a nonlinear three-point boundary value problem, Electron. J. differential equations, 34, 1-8, (1999)
[12] Ma, R., Existence theorems for a second order m-point boundary value problem, J. math. anal. appl., 211, 545-555, (1997) · Zbl 0884.34024
[13] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press San Diego, CA · Zbl 0661.47045
[14] Krasnoselskii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen
[15] Wang, H., On the existence of positive solutions for semilinear elliptic equations in annulus, J. differential equations, 109, 1-7, (1994) · Zbl 0798.34030
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.