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.


34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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[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 · Zbl 1030.39015
[6] Deiming, K., Nonlinear functional analysis, (1985), 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
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