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The Unilateral Global Bifurcation from Intervals for Fourth-Order Problems Which are Not Linearizable(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2022年01期
Page:
1-7
Research Field:
·数学·
Publishing date:

Info

Title:
The Unilateral Global Bifurcation from Intervals for Fourth-Order Problems Which are Not Linearizable
Author(s):
Shen Wenguo1; Bao Liqun2; Na Renhua1
(1.Department of Basic Courses,Lanzhou Institute of Technology,Lanzhou 730050,China)(2.Department of Electronic and Information Engineering,Lanzhou Institute of Technology,Lanzhou 730050,China)
Keywords:
fourth-order problems; global interval bifurcation; nodal solutions
PACS:
O175.8
DOI:
10.3969/j.issn.1001-4616.2022.01.001
Abstract:
In this paper,we shall establish the unilateral global bifurcation theorem which bifurcates theorem from infinity of a class of nonlinear fourth-order problems with non-differentiable nonlinearity. We shall study the existence of nodal solutions for the following problem...

References:

[1] DAI G W. Spectrum of Navier p-biharmonic problem with sign-changing weight[J]. arXiv:1207.7159vl[math.CA]31 Jul 2012.
[2]DAI G W,HAN X L. Global bifurcation and nodal solutions for fourth-order problems with sign-changing weight[J]. Applied mathematics and computation,2013,219:9399-9407.
[3]BERESTYCKI H. On some nonlinear Sturm-Liouville problem[J]. Journal of differential equations,1977,26:375-390.
[4]SCHMITT K,SMITH H L. On eigenvalue problems for nondifferentiable mappings,some aspects of nonlinear eigenvalue problems[J]. Journal of differential equations,1979,33:294-319.
[5]MA R Y,DAI G W. Global bifurcation and nodal solutions for a Sturm-Liouvilleproblem with a nonsmooth nonlinearity[J]. Journal of functional analysis,2013,265:1443-1459.
[6]DAI G W,MA R Y. Bifurcation from intervals for Sturm-Liouville problems and its applications[J]. Electronic journal of differential equations,2014(3):1-10.
[7]DAI G W,MA R R. Global bifurcation,Berestycki’s conjecture and one-sign solutions for p-Laplacian[J]. Nonlinear analysis,2013,91:51-59.
[8]SHEN W G,HE T. Unilateral global bifurcation from intervals for fourth-order problems and its applications[J]. Discrete dynamics in nature and society,2016,Article ID 5956713,15.
[9]RABINOWITZ P H. On bifurcation from infinity[J]. Journal of differential equations,1973,14:462-475.
[10]ELIAS U. Eigenvalue problems for the equations Ly+λp(x)y=0[J]. Journal of differential equations,1978,29(1):28-57.
[11]MA R Y. Nodal solutions of boundary value problem of fourth-order ordinary differential equations[J]. Journal of mathematical analysis and applications,2006,319(2):424-434.

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