Existence of multiple unbounded solutions for a three-point boundary value problems on an infinite time scales
-
Saroj Panigrahi
and
Sasmita Das
Abstract
In this paper, we consider the second-order three point boundary value problem on time scales with integral boundary conditions on a half-line. We will use the upper and lower solution method along with the Schauder’s fixed point theorem to establish the existence of at least one solution which lies between pairs of unbounded upper and lower solutions. Further, by assuming two pairs of unbounded upper and lower solutions, the Nagumo condition on the nonlinear term involved in the first-order derivative, we will establish the existence of multiple unbounded solutions on an infinite interval by using the topological degree theory. The results of this paper extend the results of Akcan and Çetin (2018), Akcan and Hamal (2014), Eloe, Kaufmann and Tisdell (2006), and generalize the results of Lian and Geng (2011). Examples are included to illustrate the validation of the results.
Funding statement: The second author was supported by University Grant Commission Fellowship, India through ref. no. 201610184291, dated February 4, 2021.
Acknowledgements
The authors are thankful to the referees for helpful suggestions and necessary corrections in completions of the paper.
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Articles in the same Issue
- Frontmatter
- Convergence of matrix transform means with respect to the Walsh–Kaczmarz system
- Analysis of the embedded cell method in 2D for the numerical homogenization of metal-ceramic composite materials
- Weighted integrability of Laguerre–Bessel transforms
- Infinitely many solutions for a p(x)-triharmonic equation with Navier boundary conditions
- Bounds of some divergence measures using Green’s function and Fink’s identity via Diamond Integrals
- Invariant pseudoparallel submanifold of an SQ-Sasakian manifolds
- Some observations on ℐ-statistically pre-Cauchy sequences of complex uncertain variables defined by Orlicz functions
- Kat\v{e}tov--Blass order and measurable filters on ℕ
- ℐ-monotonic convergence of sequences of bi-complex numbers
- On the geometry of semi-slant submanifolds of a conformal Kenmotsu manifold
- Existence of multiple unbounded solutions for a three-point boundary value problems on an infinite time scales
- A simple approach for studying stability properties of an SEIRS epidemic model
- α-, β- and γ-duals of the sequence spaces formed by a regular matrix of Tetranacci numbers
- A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces
- Recurrence relations for the joint distribution of the sum and maximum of independent random variables
- Lacunary weak convergence of sequences defined by Orlicz function
- On the stability of a double porous elastic system with visco-porous damping
