An Integral Representation of Singular Solutions and Removable Singularities of Solutions to Linear Partial Differential Equations

Ouchi, Sunao

doi:10.2977/prims/1195170733

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…In that context, the singularities of the solution are generally contained in characteristic hypersurfaces issued from the singular locus of the initial conditions. For meromorphic initial data, we may refer to [3], [8], [20], [21] and for more general ramified multivalued initial data, we may cite [9], [10], [22], [24]. In our framework, the initial data are assumed to be non singular and the coefficients of the equation now carry the singularities.…”

Section: Introductionmentioning

confidence: 99%

On Complex Singularity Analysis for Some Linear Partial Differential Equations in

Lastra

Malek²,

Stenger

2013

Abstract and Applied Analysis

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We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are singular along an analytic variety Θ in C 2 . The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea we have initiated in a previous work [16]. The solutions Y are shown to develop singularities along Θ with estimates of exponential type depending on the growth's rate of X near the singular variety. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series.

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Section: Introductionmentioning

confidence: 99%

On Complex Singularity Analysis for Some Linear Partial Differential Equations in

Lastra

Malek²,

Stenger

2013

Abstract and Applied Analysis

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show abstract

Singularities of solutions of equations with noninvolutive characteristics-I; the case of second order Fuchsian equations

Ouchi¹

1993

J. Math. Soc. Japan

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Growth property and slowly increasing behaviour of singular solutions of linear partial differential equations in the complex domain

Ouchi¹

2000

J. Math. Soc. Japan

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An Integral Representation of Singular Solutions and Removable Singularities of Solutions to Linear Partial Differential Equations

Cited by 3 publications

References 5 publications

On Complex Singularity Analysis for Some Linear Partial Differential Equations in

On Complex Singularity Analysis for Some Linear Partial Differential Equations in

Singularities of solutions of equations with noninvolutive characteristics-I; the case of second order Fuchsian equations

Growth property and slowly increasing behaviour of singular solutions of linear partial differential equations in the complex domain

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