Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions |
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Authors: | Mohamed El-Gebeily Donal O'Regan |
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Affiliation: | a Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia b Department of Mathematics, National University of Ireland, Galway, Ireland |
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Abstract: | Existence theory is developed for the equation ?(u)=F(u), where ? 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 ? 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 ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained. |
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Keywords: | Nonlinear singular differential equations Nonlinear boundary conditions Galerkin method Monotone operators |
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