barrier strips
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Author(s):  
G. V. Kuznetsov ◽  
D. V. Antonov ◽  
I. S. Voitkov ◽  
A. G. Islamova ◽  
S. S. Kropotova ◽  
...  

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 62
Author(s):  
Ravi P. Agarwal ◽  
Petio S. Kelevedjiev ◽  
Todor Z. Todorov

Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.


Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 603 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Petio S. Kelevedjiev

In this paper, we study the solvability of various two-point boundary value problems for x ( 4 ) = f ( t , x , x ′ , x ″ , x ‴ ) , t ∈ ( 0 , 1 ) , where f may be defined and continuous on a suitable bounded subset of its domain. Imposing barrier strips type conditions, we give results guaranteeing not only positive solutions, but also monotonic ones and such with suitable curvature.


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