×

Multiple positive solutions to second-order Neumann boundary value problems. (English) Zbl 1041.34013

Summary: The existence of multiple positive solutions to the second-order Neumann BVPs \[ -u''+Mu=f(t,u),\;\;u'(0)=u'(1)=0, \] and \[ u''+Mu=f(t,u),\;\;u'(0)=u'(1)=0, \] are proved by a fixed-point theorem in a cone due to Krasnosel’skii.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Dang, H.; Seth, F., Oppenheimer. Existence and uniqueness results for some nonlinear boundary value problems, J. Math. Anal. Appl., 198, 35-48 (1996) · Zbl 0855.34021
[2] Jiang, D. Q.; Liu, H. Z., Existence of positive solutions to second order Neumann boundary value problems, J. Math. Res. Exposition, 20, 3, 360-364 (2000) · Zbl 0963.34019
[3] Rachunkva, I.; Stanke, S., Topological degree method in functional boundary value problems at resonance, Nonlinear Anal. TMA, 27, 3, 271-285 (1996)
[4] Rachunkva, I., Upper and lower solutions with inverse inequality, Ann. Polon. Math., 65, 235-244 (1996)
[5] J.P. Sun, W.T. Li, Multiple positive solutions of a discrete difference system, Appl. Math. Comput., in press; J.P. Sun, W.T. Li, Multiple positive solutions of a discrete difference system, Appl. Math. Comput., in press · Zbl 1030.39015
[6] Deiming, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag New York
[7] Ma, R. Y., Existence of positive radial solutions for elliptic systems, J. Math. Anal. Appl., 201, 375-386 (1996) · Zbl 0859.35040
[8] Erbe, L. H.; Wang, H. Y., On the existence of positive solutions of ordinary differential equations, Proc. Am. Math. Soc., 120, 743-748 (1994) · Zbl 0802.34018
[9] Wang, H. Y., On the existence of positive solution for semilinear elliptic equations in the annulus, J. Differ. 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. 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.