Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line
Abstract
:1. Introduction
2. Definitions and Auxiliary Results
- (i)
- For each , is measurable on
- (ii)
- For almost every is continuous in
- (iii)
- For each , there exists a positive function , such that whenever satisfies , , one has
- 1.
- All functions from M are uniformly bounded;
- 2.
- All functions from M are equicontinuous on any compact interval of ;
- 3.
- All functions from M are equiconvergent at infinity, that is, for any given , there exists a such that, for
- (H1)
- For is nondecreasing in all the arguments except in the variable;
- (H2)
- for and
- (H3)
- is nondecreasing on w for fixed z.
3. Main Result
4. Example
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Minhós, F.; Coxe, I. Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line. Mathematics 2021, 9, 499. https://doi.org/10.3390/math9050499
Minhós F, Coxe I. Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line. Mathematics. 2021; 9(5):499. https://doi.org/10.3390/math9050499
Chicago/Turabian StyleMinhós, Feliz, and Infeliz Coxe. 2021. "Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line" Mathematics 9, no. 5: 499. https://doi.org/10.3390/math9050499
APA StyleMinhós, F., & Coxe, I. (2021). Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line. Mathematics, 9(5), 499. https://doi.org/10.3390/math9050499