Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Mohamed El-Gebeily; Donal O'Regan

doi:10.1016/j.jmaa.2006.12.040

Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Mohamed El-Gebeily^*
, Donal O'Regan

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Existence theory is developed for the equation ℓ (u) = F (u), where ℓ is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ℓ to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ℓ in the singular case is investigated. A special class of self-adjoint operators associated with ℓ is obtained.

Original language	English
Pages (from-to)	140-156
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	334
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.12.040
State	Published - 1 Oct 2007

Bibliographical note

Funding Information:
Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

Keywords

Galerkin method
Monotone operators
Nonlinear boundary conditions
Nonlinear singular differential equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2006.12.040

Cite this

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title = "Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions",

abstract = "Existence theory is developed for the equation ℓ (u) = F (u), where ℓ is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ℓ to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ℓ in the singular case is investigated. A special class of self-adjoint operators associated with ℓ is obtained.",

keywords = "Galerkin method, Monotone operators, Nonlinear boundary conditions, Nonlinear singular differential equations",

author = "Mohamed El-Gebeily and Donal O'Regan",

note = "Funding Information: Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.",

year = "2007",

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doi = "10.1016/j.jmaa.2006.12.040",

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T1 - Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

AU - El-Gebeily, Mohamed

AU - O'Regan, Donal

N1 - Funding Information: Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

PY - 2007/10/1

Y1 - 2007/10/1

N2 - Existence theory is developed for the equation ℓ (u) = F (u), where ℓ is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ℓ to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ℓ in the singular case is investigated. A special class of self-adjoint operators associated with ℓ is obtained.

AB - Existence theory is developed for the equation ℓ (u) = F (u), where ℓ is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ℓ to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ℓ in the singular case is investigated. A special class of self-adjoint operators associated with ℓ is obtained.

KW - Galerkin method

KW - Monotone operators

KW - Nonlinear boundary conditions

KW - Nonlinear singular differential equations

UR - https://www.scopus.com/pages/publications/34249306532

U2 - 10.1016/j.jmaa.2006.12.040

DO - 10.1016/j.jmaa.2006.12.040

M3 - Article

AN - SCOPUS:34249306532

SN - 0022-247X

VL - 334

SP - 140

EP - 156

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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