Chai, Guoqing Existence of positive solutions for fourth-order boundary value problem with variable parameters. (English) Zbl 1113.34008 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 4, 870-880 (2007). Summary: By using a fixed-point theorem and an operator spectral theorem, the author establishes the existence of positive solutions for the fourth-order boundary value problem: \[ \begin{cases} u^{(4)}+B(t)u''-A(t)u=f(t,u), \quad 0<t<1\\ u(0)=u(1)= u''(0)=u''(1)=0\end{cases} \] where \(A(t)\), \(B(t)\in C[0,1]\) and \(f(t,u):[0,1] \times [0,\infty)\to[0,\infty)\) are continuous. Cited in 22 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations Keywords:positive solutions; fixed point theorem; operator spectral PDFBibTeX XMLCite \textit{G. Chai}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 4, 870--880 (2007; Zbl 1113.34008) Full Text: DOI References: [1] Gupta, C. P., Existence and uniqueness theorems for a bending of an elastic beam equation, Appl. Anal., 26, 289-304 (1988) · Zbl 0611.34015 [2] Gupta, C. P., Existence and uniqueness results for the bending of an elastic beam equation at resonance, J. Math. Anal. Appl., 135, 208-225 (1988) · Zbl 0655.73001 [3] Yang, Y., Fourth-order two-point boundary value problems, Proc. Amer. Math. Soc., 104, 175-180 (1988) · Zbl 0671.34016 [4] Del Pino, M. A.; Manasevich, R. F., Existence for a fourth-order boundary value problem under a two parameter nonresonance condition, Proc. Amer. Math. Soc., 112, 81-86 (1991) · Zbl 0725.34020 [5] De Coster, C.; Fabry, C.; Munyamarere, F., Nonresonance conditions for fourth-order nonlinear boundary value problems, Internat. J. Math. Math. Sci., 17, 725-740 (1994) · Zbl 0810.34017 [6] Ma, R.; Wang, H., On the existence of positive solutions of fourth-order ordinary differential equations, Appl. Anal., 59, 225-231 (1995) · Zbl 0841.34019 [7] Ma, R.; Zhang, J.; Fu, S., The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl., 215, 415-422 (1997) · Zbl 0892.34009 [8] Bai, Z., The method of lower and upper solutions for a bending of an elastic beam equation, J. Math. Anal. Appl., 248, 195-202 (2000) · Zbl 1016.34010 [9] Li, Y. X., Positive solutions of fourth-order boundary value problems with two parameters, J. Math. Anal. Appl., 281, 477-484 (2003) · Zbl 1030.34016 [10] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press New York · Zbl 0661.47045 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.