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On Some Elliptic Equations with Nonlocal Nonlinear Terms(Solutions for Nonlinear Elliptic Equations)

open access: yesOn Some Elliptic Equations with Nonlocal Nonlinear Terms(Solutions for Nonlinear Elliptic Equations)
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Identification of nonlinear elliptic equations

Applied Mathematics & Optimization, 1996
The authors study the identification of the nonlinearities \(a\) and \(b\) in the following boundary value problems: \[ -\text{div}(a(\nabla y))\ni f\quad\text{in }\Omega,\quad y=0\quad\text{on }\partial\Omega \] and \[ -\Delta y+b(y)\ni f\quad\text{in }\Omega,\quad y=0\quad\text{on }\partial\Omega, \] where \(\Omega\) is a bounded domain in \(\mathbb ...
Barbu, V., Kunisch, K.
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Nonlinear Singular Elliptic Equations

Journal of the London Mathematical Society, 1989
Let F be a dense vector subspace of a Banach space E, and f be a functional defined on F, in which f is not expected to have any critical point. We extend the variational theory to seek generalized critical points of f in E (not in F). Using these results we find solutions in \(W_ 0^{1,2}(\Omega)\) of the following equation \[ (P)\quad -\Delta u+c=Ke ...
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ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS

Mathematics of the USSR-Sbornik, 1984
Translation from Mat. Sb. Nov. Ser. 120(162), No.3, 311-330 (Russian) (1983; Zbl 0525.35038).
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