2013
DOI: 10.7153/dea-05-02
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Matching method for nodal solutions of multi-point boundary value problems

Abstract: Abstract. In this paper, we study the nonlinear boundary value problem consisting of the equation y + w(t) f (y) = 0 on [a,b] and two multi-point boundary conditions. We establish the existence of various nodal solutions of this problem by matching the solutions of two boundary value problems, each of which involves one separated boundary condition and one multi-point boundary condition, at some point in (a,b) . We also obtain conditions for this problem not to have certain types of nodal solutions.Mathematics… Show more

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Cited by 3 publications
(6 citation statements)
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“…For the problem (4.4) with standard (single-point) boundary conditions, it is shown in [8] that, for each k 0, 6) with N k = S k . That is, the nodal properties of the solutions are preserved along each continuum C k .…”
Section: 2mentioning
confidence: 99%
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“…For the problem (4.4) with standard (single-point) boundary conditions, it is shown in [8] that, for each k 0, 6) with N k = S k . That is, the nodal properties of the solutions are preserved along each continuum C k .…”
Section: 2mentioning
confidence: 99%
“…Various types of boundary value problems with multi-point boundary conditions, both linear and nonlinear, have been extensively studied recently, see for example, [2][3][4][5][6][7][12][13][14][15][16], and the references therein. In this paper we will continue the investigation of the spectral properties of the linear problem (1.2)-(1.3), and then apply these properties to the nonlinear problem (1.1)-(1.2).…”
Section: Introductionmentioning
confidence: 99%
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“…where r = |x| and = d dr . Motivated by the previous results [6,14,17,25,35,37], we study two issues related to (1.2)-(1.3). When w > 0, we investigate the existence of sign-changing solutions with the prescribed number of zeros in a finite interval.…”
Section: Introductionmentioning
confidence: 99%
“…Nonlinear BVPs with nonlocal BCs, including multi‐point BCs, have also received a lot of attention in research, and various conditions are obtained for the existence of positive solutions and nodal solutions. We refer the reader to and the references therein for some recent work on this topic.…”
Section: Introductionmentioning
confidence: 99%