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Bifurcation techniques for Lidstone boundary value problems. (English) Zbl 1140.34321
Summary: By employing bifurcation techniques, this paper investigates the existence of nontrivial solutions (single and multiple) for Lidstone boundary value problems $$\cases (-1)^n u^{(2n)}(t)=f(t,u(t),u''(t),\dots,u^{(2(n-1))}(t)),\quad & t\in (0,1);\\ u^{(2i)}(0)=u^{(2i)}(1)=0, & i=0,1,\dots,n-1.\endcases$$ Our results improve on those in the literature.

34B15Nonlinear boundary value problems for ODE
34C23Bifurcation (ODE)
Full Text: DOI
[1] Agarwal, R. P.; O’regan, D.; Stanek, S.: Singular lidstone boundary value problem with given maximal values for solutions, Nonlinear anal. 55, 859-881 (2003) · Zbl 1055.34040 · doi:10.1016/j.na.2003.06.001
[2] Avery, R. I.; Davis, J. M.; Henderson, J.: Three symmetric positive solutions for lidstone problems by a generalization of the Leggett--Williams theorem, Electron. J. Differential equations 40, 1-15 (2000) · Zbl 0958.34020 · emis:journals/EJDE/Volumes/2000/40/abstr.html
[3] Bai, Z.; Ge, W.: Solutions of 2nth lidstone boundary value problems and dependence on higher order derivatives, J. math. Anal. appl. 279, 442-450 (2003) · Zbl 1029.34019 · doi:10.1016/S0022-247X(03)00011-8
[4] Guo, D.; Sun, J.: Nonlinear integral equations, (1987)
[5] Davis, J. M.; Henderson, J.; Wong, P. J. Y.: General lidstone problems: multiplicity and symmetry of solutions, J. math. Anal. appl. 251, 527-548 (2000) · Zbl 0966.34023 · doi:10.1006/jmaa.2000.7028
[6] Liu, Y.: Structure of a class of singular boundary value problem with superlinear effect, J. math. Anal. appl. 284, 64-75 (2003) · Zbl 1042.34041 · doi:10.1016/S0022-247X(03)00214-2
[7] Liu, Y.: On multiple positive solutions of nonlinear singular boundary value problem for fourth order equations, Appl. math. Lett. 17, 747-757 (2004) · Zbl 1073.34018 · doi:10.1016/j.aml.2004.06.001
[8] Ma, R.: Nodal solutions for a fourth-order two-point boundary value problems, J. math. Anal. appl. 314, 254-265 (2006) · Zbl 1085.34015 · doi:10.1016/j.jmaa.2005.03.078
[9] Ma, Y.: Existence of positive solutions of lidstone boundary value problems, J. math. Anal. appl. 314, 97-108 (2006) · Zbl 1085.34021 · doi:10.1016/j.jmaa.2005.03.059
[10] Rabinowitz, P. H.: Some global results for nonlinear eigenvalue problems, J. funct. Anal. 7, 487-513 (1971) · Zbl 0212.16504 · doi:10.1016/0022-1236(71)90030-9
[11] Rabinowitz, P. H.: On bifurcation from infinity, J. differential equations 14, 462-475 (1973) · Zbl 0272.35017 · doi:10.1016/0022-0396(73)90061-2
[12] Rynne, B. P.: Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems, J. differential equations 188, 461-472 (2003) · Zbl 1029.34015 · doi:10.1016/S0022-0396(02)00146-8
[13] Wang, Y.: On 2nth-order lidstone boundary value problems, J. math. Anal. appl. 312, 383-400 (2005) · Zbl 1090.34015 · doi:10.1016/j.jmaa.2005.03.039
[14] Yao, Q.: On the positive solutions of lidstone boundary value problems, Appl. math. Comput. 137, 477-485 (2003) · Zbl 1093.34515 · doi:10.1016/S0096-3003(02)00152-2
[15] Zhang, B.; Liu, X.: Existence of multiple symmetric positive solutions of higher order lidstone problems, J. math. Anal. appl. 284, 672-689 (2003) · Zbl 1048.34054 · doi:10.1016/S0022-247X(03)00386-X