Gao, Yunzhu; Pei, Minghe Solvability for two classes of higher-order multi-point boundary value problems at resonance. (English) Zbl 1149.34008 Bound. Value Probl. 2008, Article ID 723828, 14 p. (2008). Summary: Using the theory of coincidence degree, we establish existence results of positive solutions for higher-order multi-point boundary value problems at resonance for ordinary differential equation\[ u(n)(t)=f(t,u(t),u'(t),\dots,u^{(n-1)}(t))+e(t),\quad t\in (0,1), \]with one of the following boundary conditions:\[ u^{(i)}(0)=0,\quad i=1,2,\dots, n-2, u^{(n-1)}(0)=u^{(n-1)}(\xi), u^{(n-2)}(1)=\sum_{j=1}^{m-2}\beta_ju^{(n-2)}(\eta_j), \] and \[ u(i)(0)=0,\quad i=1,2,\dots, n-1,\quad u^{(n-2)}(1)=\sum_{j=1}^{m-2}\beta_ju^{(n-2)}(\eta_j), \]where \(f:[0,1]\times\mathbb R^n\to \mathbb =(-\infty,+\infty)\) is a continuous function, \(e(t)\in L^1[0,1]\beta_j\in\mathbb R\) \((1\leq j\leq m-2, m\geq 4)\), \(0<\eta 1<\eta^2<\cdots <\eta_{m-2}<1\), \(0<\xi<1,\) all the \(\beta_{-j}^{-s}\) have not the same sign. We also give some examples to demonstrate our results. Cited in 3 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations PDFBibTeX XMLCite \textit{Y. Gao} and \textit{M. Pei}, Bound. Value Probl. 2008, Article ID 723828, 14 p. (2008; Zbl 1149.34008) Full Text: DOI EuDML References: [1] doi:10.1016/j.jmaa.2004.02.001 · Zbl 1053.34017 · doi:10.1016/j.jmaa.2004.02.001 [2] doi:10.1016/j.jmaa.2004.08.012 · Zbl 1072.34012 · doi:10.1016/j.jmaa.2004.08.012 [3] doi:10.1006/jmaa.1997.5520 · Zbl 0883.34020 · doi:10.1006/jmaa.1997.5520 [4] doi:10.1016/S0096-3003(97)81653-0 · Zbl 0910.34032 · doi:10.1016/S0096-3003(97)81653-0 [5] doi:10.1016/0362-546X(94)90137-6 · Zbl 0815.34012 · doi:10.1016/0362-546X(94)90137-6 [6] doi:10.1006/jmaa.1995.1036 · Zbl 0819.34012 · doi:10.1006/jmaa.1995.1036 [7] doi:10.1016/S0096-3003(01)00036-4 · Zbl 1054.34033 · doi:10.1016/S0096-3003(01)00036-4 [8] doi:10.1016/S0096-3003(02)00050-4 · Zbl 1053.34016 · doi:10.1016/S0096-3003(02)00050-4 [9] doi:10.1006/jmaa.2000.7320 · Zbl 0988.34009 · doi:10.1006/jmaa.2000.7320 [10] doi:10.1006/jmaa.1995.1348 · Zbl 0847.34026 · doi:10.1006/jmaa.1995.1348 [11] doi:10.1016/S0022-247X(03)00567-5 · Zbl 1046.34029 · doi:10.1016/S0022-247X(03)00567-5 [13] doi:10.1007/BFb0085076 · doi:10.1007/BFb0085076 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.