Results 131 to 140 of about 2,594 (170)
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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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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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Solvability of an Elliptic Equation with a Gradient Nonlinearity
Differential Equations, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a Nonlinear Elliptic Equation with Periodic Coefficients
SIAM Journal on Applied Mathematics, 1981Homogenization is applied to a mildly nonlinear equation which arises in chemical kinetics. The method of multiple scales is used to get the homogenized equation, and the convergence is proved using the energy method.
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ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS. II
Mathematics of the USSR-Sbornik, 1984zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear Elliptic Equations with Mixed Singularities
Potential Analysis, 2017This 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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Identification of nonlinear elliptic equations
Applied Mathematics & Optimization, 1996The 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, 1987The 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, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear elliptic and parabolic equations
Journal of Soviet Mathematics, 1979Results 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, 1997The 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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