Results 201 to 210 of about 16,559 (211)

Positive Solutions of Quasilinear Elliptic Equations

Mathematical Notes, 2005
The author studies the existence of radially symmetric solutions of the problem \[ -\Delta_p \varphi = \lambda\varphi^q - | \nabla\varphi| ^s \quad\text{in}\quad B, \qquad \varphi > 0 \quad\text{in}\quad B, \qquad \varphi = 0 \quad\text{on}\quad \partial B, \tag \(*\) \] where \(\Delta_p\varphi = \text{div}(| \nabla\varphi| ^{p-2}\nabla\varphi)\), \(p ...
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An Eigenvalue Problem for a Quasilinear Elliptic Equation

Mathematische Nachrichten, 1998
AbstractIn this paper, we are concerned with the following eigenvalue problem: here Ω is a C1,α‐domain and Δp is the degenerate p‐Laplace operator with p > 1. An interesting special case is when f = π(χ)|u|σ1−1 u+ϕ(χ)|u|σ−1u, 0 < q1 <q2. By using the sub‐ and supersolutions method and the variational method, we prove the existence of the ...
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Some remarks on a system of quasilinear elliptic equations

NoDEA : Nonlinear Differential Equations and Applications, 2002
The present paper deals with the functional \[ \Phi(u,v)= {1\over p} \int_\Omega |\nabla u|^p+ {1\over q}\int_\Omega|\nabla v|^q-\int_\Omega F(x,u,v)\,dx, \tag{1} \] where \(p\) and \(q\) are real numbers larger than \(1,\Omega\) is some bounded domain in \(\mathbb R^N\), \(u\) and \(v\) are real-valued functions defined in \(\overline\Omega\) and ...
BOCCARDO, Lucio, D. De Figueiredo
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THE EIGENVALUE PROBLEM OF QUASILINEAR ELLIPTIC EQUATION

Acta Mathematica Scientia, 1991
The nonlinear eigenvalue problem \(-\Delta_ p u+\lambda| u|^{p-2}u=f(x,u)\) in \(\mathbb{R}^ N\), with \(u\in W^{1,p}(\mathbb{R}^ N)\) is studied in this paper. Here \(p>1\), \(\lambda\) is a real parameter, and \(\Delta_ p u=\text{div}(|\nabla u|^{p-2}\nabla u)\) is the so-called \(p\)-Laplacian.
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Geometric problems in quasilinear elliptic equations

Russian Mathematical Surveys, 1970
In their survey reports A. D. Aleksandrov and A. V. Pogorelov [1] and N. V. Efimov [2] give a detailed account of the deep relationships between the theory of surfaces and the theory of partial differential equations; they also highlight the main results and research problems on the boundary of geometry and analysis connected with Gaussian curvature of
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On Blow Up Solutions of a Quasilinear Elliptic Equation

Mathematische Nachrichten, 2000
The existence and asymptotic behaviour of the solutions of the equation \(\Delta u + |Du|^q =f(u)\) in a bounded and regular domain in \({\mathbb{R}}^N\) which diverge on \(\partial \Omega\), is studied.
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Remarks on some quasilinear elliptic equations [PDF]

Communications on Pure and Applied Mathematics, 1975
Jerry L. Kazdan, F. W. Warner
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QUASILINEAR ELLIPTIC-PARABOLIC EQUATIONS

Mathematics of the USSR-Sbornik, 1968
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QUASILINEAR ELLIPTIC DIFFERENTIAL EQUATIONS [PDF]

Bulletin of the London Mathematical Society, 1979
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LINEAR AND QUASILINEAR ELLIPTIC EQUATIONS

Bulletin of the London Mathematical Society, 1969
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