6533b824fe1ef96bd127fe42

RESEARCH PRODUCT

On Some Properties of the Dirichlet Problem at Resonance

Arnold Lepin

subject

CombinatoricsDirichlet problemsymbols.namesakeMathematics Subject ClassificationGeneral MathematicsBounded functionDirichlet boundary conditionFree boundary problemsymbolsBoundary value problemFunction (mathematics)Elliptic boundary value problemMathematics

description

Abstract The boundary value problem at resonance 𝑥″ + 𝑥 = 𝑞 sin 𝑡 + 𝑓(𝑡,𝑥,𝑥′), 𝑥(0) = 0, 𝑥(π) = 0, is considered, where 𝑓 : [0,π] × 𝑹2 → 𝑹 is a bounded Carathéodory function, 𝑞 is a parameter. We state the multiplicity results without assuming that 𝑓 has limits.

https://doi.org/10.1515/gmj.2008.111