A fixed point theorem, a perturbed differential equation, and a multivariable Volterra integral equation

Lovelady, David Lowell

doi:10.1090/s0002-9947-1973-0336263-9

Trans. Amer. Math. Soc.

1973

DOI: 10.1090/s0002-9947-1973-0336263-9

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A fixed point theorem, a perturbed differential equation, and a multivariable Volterra integral equation

David Lowell Lovelady¹

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2012

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Cited by 7 publications

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“…xn =/. Recently, Lovelady announced (in [7]) results concerning the existence and uniqueness of solutions to a Banach space analog of system (III) where/is assumed to have a continuous Fréchet derivative. In [8], this author showed that condition (I) is satisfied by all points in a dense subset of X whenever A is the infinitesimal generator of a strongly continuous semigroup of bounded linear transformations.…”

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confidence: 99%

Product Integral Techniques for Abstract Hyperbolic Partial Differential Equations

Spellmann¹

1975

Transactions of the American Mathematical Society

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ABSTRACT. Explicit and implicit product integral techniques are used to represent a solution U to the abstract system: £/i2(x, y) = AU(x, y); U(x, 0) = p = U(0, y). The coefficient A is a closed linear transformation defined on a dense subspace D(A) of the Banach space X and the point p in D(A) satisfies the condition that WA'pW < S'(i\)3/2 for all integers i > 0 and some S > 0. The implicit technique is developed under the additional assumption that A generates a strongly continuous semigroup of bounded linear transformations on X. Both methods provide representations for the Jq Bessel function.

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confidence: 99%

Product Integral Techniques for Abstract Hyperbolic Partial Differential Equations

Spellmann¹

1975

Transactions of the American Mathematical Society

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A note on differential and integral equations in the spaces of functions of -bounded variation

Bugajewska¹

2012

Nonlinear Analysis: Theory, Methods & Applications

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Mappings of higher order and nonlinear equations in some spaces of almost periodic functions

Bugajewski

Gan

Kasprzak

2012

Nonlinear Analysis: Theory, Methods & Applications

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A fixed point theorem, a perturbed differential equation, and a multivariable Volterra integral equation

Cited by 7 publications

References 20 publications

Product Integral Techniques for Abstract Hyperbolic Partial Differential Equations

Product Integral Techniques for Abstract Hyperbolic Partial Differential Equations

A note on differential and integral equations in the spaces of functions of -bounded variation

Mappings of higher order and nonlinear equations in some spaces of almost periodic functions

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