Well-posedness of the second-order linear singular Dirichlet problem

Alexander Lomtatidze; Zdeněk Opluštil

doi:10.1515/gmj-2015-0023

Published by De Gruyter May 8, 2015

Well-posedness of the second-order linear singular Dirichlet problem

Alexander Lomtatidze and Zdeněk Opluštil

From the journal Georgian Mathematical Journal

https://doi.org/10.1515/gmj-2015-0023

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Abstract

Conditions guaranteeing well-posedness of the problem u''=p0(t)u+q0(t), u(a)=0, u(b)=0, are established. Here p0,q0:]a,b[→ℝ are locally Lebesgue integrable functions and may have singularities at t=a and t=b.

Keywords: Singular Dirichlet problem; well-posedness

MSC: 34B05; 34B08

Funding source: Faculty of Mechanical Engineering, Brno University of Technology

Award Identifier / Grant number: FSI-S-14-2290

Funding source: RVO

Award Identifier / Grant number: 67985840

Received: 2014-11-24

Accepted: 2015-2-24

Published Online: 2015-5-8

Published in Print: 2015-9-1

Well-posedness of the second-order linear singular Dirichlet problem

Abstract

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