Results 281 to 290 of about 8,945 (319)

Nonlinear Elliptic Equations

1996
Methods of the calculus of variations applied to problems in geometry and classical continuum mechanics often lead to elliptic PDE that are not linear. We discuss a number of examples and some of the developments that have arisen to treat such problems.
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Nonlinear Elliptic Equations with Mixed Singularities

Potential Analysis, 2017
This paper deals with the mathematical analysis of a class of non-variational degenerate elliptic equations with mixed singular structures. A feature of the paper under review is that the singular structure arises both at the set of critical points and on the ground touching points. The main result of this paper establishes that positive solutions have
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ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS. II

Mathematics of the USSR-Sbornik, 1984
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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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An elliptic equation with singular nonlinearity

Communications in Partial Differential Equations, 1987
The purpose of this paper is to study the problem (P) −Δu+u−α=f in Ω, u=0 on ∂Ω, u−α∈L1(Ω), u>0 in Ω, where Ω is a bounded smooth open set of RN, f≥0, f∈L1(Ω) and ...
J. I. Diaz, J.M. Morel, L. Oswald
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Nonlinear elliptic equations for measures

Doklady Mathematics, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear elliptic and parabolic equations

Journal of Soviet Mathematics, 1979
Results of recent years are presented on the theory of nonlinear elliptic and parabolic equations of any order including equations of infinite order.
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On a singular nonlinear elliptic equation

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author studies the existence of positive solutions \(u\in C^2(B_R)\cap C^1(\overline B_R)\) of the following singular Dirichlet problem: \[ u^\alpha(\Delta u+u)- u/\alpha= 0,\quad x\in B_R,\quad u(x)=0,\quad x\in \partial B_R.
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Nonlinear equations and elliptic curves

Journal of Soviet Mathematics, 1985
This paper deals with the algebro-geometric or finite zone solution of noninear equations which can be written as zero curvature equation \(U_ t-V_ x+[U,V]=0\), where U(x,t,\(\lambda)\) and V(x,t,\(\lambda)\) are two matrices and the parameter \(\lambda\) is defined on elliptic curves. The author presents the main idea of global finite-zone integration
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A boundary expansion of solutions to nonlinear singular elliptic equations

Science China Mathematics, 2021
Jian Lu, Xu-Jia Wang, Wang Xu-Jia
exaly