Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
-
Alberto Cabada
,
Rochdi Jebari
Abstract
In this paper, we study the existence of positive solutions for a fourth order boundary value problem coupled to functional perturbed clamped beam boundary conditions. Our main ingredient is the classical fixed point index. The problem investigated is an extension of other problems studied in previous papers by covering very general nonlocal perturbed conditions on the boundary.
First and third authors were supported by Grant PID2020-113275GB-I00, funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe” of the “European Union”, and by Xunta de Galicia (Spain), project ED431C 2023/12.
Communicated by Jozef Džurina
References
[1] Bai, Z.—Wang, H.: On the positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl. 270 (2002), 357–368.10.1016/S0022-247X(02)00071-9Search in Google Scholar
[2] Bonanno, G.—Bella, B. D.: A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl. 343 (2008), 1166–1176.10.1016/j.jmaa.2008.01.049Search in Google Scholar
[3] Cabada, A.—Cid, J. A.—Sanchez, L.: Positivity and lower and upper solutions for fourth order boundary value problems, Nonlinear Anal. 67 (2007), 1599–1612.10.1016/j.na.2006.08.002Search in Google Scholar
[4] Cabada, A.—Enguiça, R. R.: Positive solutions of fourth order problems with clamped beam boundary conditions, Nonlinear Anal. 74 (2011), 3112–3122.10.1016/j.na.2011.01.027Search in Google Scholar
[5] Cabada, A.—Jebari, R.: Existence results for a clamped beam equation with integral boundary conditions, Electron. J. Qual. Theory Differential Equ. (2020), Art. No. 70.10.14232/ejqtde.2020.1.70Search in Google Scholar
[6] Cabada, A.—López-Somoza, L.—Yousfi, M.: Existence of solutions of nonlinear systems subject to arbitrary linear non-local boundary conditions, J. Fixed Point Theory Appl. 25(4) (2023), Art. No. 81. %24 pp.10.1007/s11784-023-01083-7Search in Google Scholar
[7] Cabada, A.—Saavedra, L.: Disconjugacy characterization by means of spectral (k, n – k) problems, Appl. Math. Lett. 52 (2016), 21–29.10.1016/j.aml.2015.08.007Search in Google Scholar
[8] Coppel, W. A.: Disconjugacy. Lecture Notes in Math., Vol. 220, Springer-Verlag, Berlin-New York, 1971.10.1007/BFb0058618Search in Google Scholar
[9] Deimling, K.: Nonlinear Functional Analysis, Springer, Berlin, 1985.10.1007/978-3-662-00547-7Search in Google Scholar
[10] Gazzola, F.: Mathematical Models for Suspension Bridges: Nonlinear Structural Instability. Modeling, Simulations and Applications, Vol. 15, Springer, 2015.10.1007/978-3-319-15434-3Search in Google Scholar
[11] Graef, J. R.—Henderson, J.—Yang, B.: Positive solutions to a fourth-order three point boundary value problem, Discrete Contin. Dyn. Syst. Supplement (2009), 269–275.Search in Google Scholar
[12] Graef, J. R.—Yang, B.: Existence and nonexistence of positive solutions of fourth order nonlinear boundary-value problems, Appl. Anal. 74 (2000), 201–214.10.1080/00036810008840810Search in Google Scholar
[13] Guo, D.—Lakshmikantham, V.: Nonlinear Problems in Abstract Cones, Academic Press, Boston, 1988.Search in Google Scholar
[14] Lan, K. Q.: Multiple positive solutions of semilinear differential equations with singularities, J. London Math. Soc. (2) 63 (2001) 690–704.10.1112/S002461070100206XSearch in Google Scholar
[15] Ma, R.—Jihui, Z.—Shengmao, F.: The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl. 215 (1997), 415–422.10.1006/jmaa.1997.5639Search in Google Scholar
[16] Webb, J. R. L.: Remarks on positive solutions of three point boundary value problems, Dynamical Systems and Differential Equations, Wilmington, NC, 2002, Discrete and Continuous Dynamical Systems, suppl. (American Institute of Mathematical Sciences, Springfield, MO, 2003) 905–915.Search in Google Scholar
© 2024 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- 10.1515/ms-2024-frontmatter4
- Intervals of posets of a zero-divisor graph
- Coalgebraic methods for Ramsey degrees of unary algebras
- On nonexistence of D(n)-quadruples
- Rees short exact sequences and preenvelopes
- Generalized discrete Grüss and related results with applications
- Radius problem associated with certain ratios and linear combinations of analytic functions
- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
- On a solvable four-dimensional system of difference equations
- Euclidean operator radius inequalities of d-tuple operators and operator matrices
- Equable parallelograms on the Eisenstein lattice
- On certain star versions of the Hurewicz property using ideals
- Relative versions of star-Menger property
- The Maxwell-Boltzmann-Exponential distribution with regression model
- New results for the Marshall-Olkin family of distributions
- A new family of copulas based on probability generating functions
- Induced mappings on the hyperspace of totally disconnected sets
Articles in the same Issue
- 10.1515/ms-2024-frontmatter4
- Intervals of posets of a zero-divisor graph
- Coalgebraic methods for Ramsey degrees of unary algebras
- On nonexistence of D(n)-quadruples
- Rees short exact sequences and preenvelopes
- Generalized discrete Grüss and related results with applications
- Radius problem associated with certain ratios and linear combinations of analytic functions
- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
- On a solvable four-dimensional system of difference equations
- Euclidean operator radius inequalities of d-tuple operators and operator matrices
- Equable parallelograms on the Eisenstein lattice
- On certain star versions of the Hurewicz property using ideals
- Relative versions of star-Menger property
- The Maxwell-Boltzmann-Exponential distribution with regression model
- New results for the Marshall-Olkin family of distributions
- A new family of copulas based on probability generating functions
- Induced mappings on the hyperspace of totally disconnected sets
