On the Solvability of Boundary Value Problems for an Abstract Bessel-Struve Equation

We consider the Dirichlet and Neumann boundary value problems for the hyperbolic Bessel-Struve equation u″ ( t ) + kt −1 ( u′ ( t ) - u′ (0)) = Au ( t ) on the half-line t > 0, where k > 0 is a parameter and A is a densely defined closed linear operator in a complex Banach space E . Generally...

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Bibliographic Details
Published in:Differential equations 2019-08, Vol.55 (8), p.1069-1076
Main Author: Glushak, A. V.
Format: Article
Language:English
Subjects:
Banach spaces
Boundary value problems
Difference and Functional Equations
Differential equations
Dirichlet problem
Linear operators
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We consider the Dirichlet and Neumann boundary value problems for the hyperbolic Bessel-Struve equation u″ ( t ) + kt −1 ( u′ ( t ) - u′ (0)) = Au ( t ) on the half-line t > 0, where k > 0 is a parameter and A is a densely defined closed linear operator in a complex Banach space E . Generally speaking, these problems are ill posed. We establish sufficient conditions on the operator coefficient A and the boundary elements for these problems to be uniquely solvable.
ISSN:0012-2661
1608-3083
DOI:10.1134/S001226611908007X