Nonnegative solutions for a class of fourth order singular eigenvalue problems
DOI:
https://doi.org/10.24193/subbmath.2024.4.14Keywords:
Fixed point, fourth-order boundary value problem, positive solution, coneAbstract
In this paper, we discuss the existence of nonnegative solutions to a fourth order singular boundary value problem at two points. Our result is based on a recent Birkhoff-Kellogg type fixed point theorem developed on translates of a cone on a Banach space.References
Bai, Z., The method of lower and upper solutions for a bending of an elastic beam
equation, J. Math. Anal. Appl., 248(2000), no. 1, 195-202.
Bai, Z., Wang, H., On positive solutions of some nonlinear fourth-order beam equations,
J. Math. Anal. Appl., 270(2002), no. 2, 357-368.
Benslimane, S., Georgiev, S.G., Mebarki, K., Multiple nonnegative solutions for a of
class fourth-order BVPs via a new topological approach, Adv. Theory Nonlinear Anal.
Appl., 6(2022), no. 3, 390-404.
Bouchal, L., Georgiev, S.G., Mebarki, K., On the existence of solutions for a class of
nonlinear fully fourth order differential system, Proyecciones, 43(2024), no. 3, 613-629.
Calamai, A., Infante, G., An a ne Birkho -Kellogg-type result in cones with applications
to functional differential equations, Math. Methods Appl. Sci., (2022), 1-9.
Calamai, A., Infante, G., On fourth order retarded equations with functional boundary
conditions: A uni ed approach, Discrete Contin. Dyn. Syst. - S, Early access January
Feng, M., Ge, W., Existence of positive solutions for singular eigenvalue problems, Elec-
tron. J. Differential Equations, 2006(2006), no. 105, 1-9.
Han, G., Xu, Z., Multiple solutions of some nonlinear fourth-order beam equations, Non-
linear Anal., 68(2008), no. 12, 3646-3656.
Liu, B., Positive solutions of fourth-order two point boundary value problems, Appl.
Math. Comput., 148(2004), no. 2, 407-420.
Ma, R., Wang, H., On the existence of positive solutions of fourth-order ordinary differ-
ential equations, Appl. Anal., 59(1995), no. 1-4, 225-231.
Pang, C., Dong, W., Wei, Z., Multiple solutions for fourth-order boundary value problem,
J. Math. Anal. Appl., 314(2006), no. 2, 464-476.
Yao, Q., Positive solutions for eigenvalue problems of fourth-order elastic beam equa-
tions, Appl. Math. Lett., 17(2004), no. 2, 237-243.
Zhu, Y., Weng, P., Multiple positive solutions for a fourth-order boundary value problem,
Bol. Soc. Parana. Mat., 21(2003), no. 1-2, 9-19.
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