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On quasilinear elliptic equations in \(\mathbb{R}^N\)

, 1996
Summary: We give a result for the \(p\)-Laplacian operator complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation \(-\Delta u= h(x)u^q\) in \(\mathbb{R}^N\), where \(0 ...
Alves, C. O., Concalves, J. V., Maia, L. A.   +2 more
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On Some Quasilinear Elliptic Equations

On Some Quasilinear Elliptic Equations
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An Inverse Problem for a Quasilinear Elliptic Equation

Journal of Mathematical Sciences, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lyubanova, A. Sh., Velisevich, A. V.
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Quasilinear Elliptic Equations with Morrey Data

Proceeding of the Bulgarian Academy of Sciences, 2013
We obtain global essential boundedness and Holder continuity of the weak solutions to quasilinear elliptic equations in divergence form with data lying in Morrey spaces.
BYUN S. S., PALAGACHEV, Dian Kostadinov
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BIFURCATIONS FOR QUASILINEAR ELLIPTIC EQUATIONS, II

Communications in Contemporary Mathematics, 2008
This paper is concerned with bifurcation solutions of quasilinear elliptic problems. Our results generalize some earlier work, in particular, a similar type of result found in [3] where an additional structural condition is required to be imposed and the result in [11] where bifurcations in terms of the radius of the solutions were considered.
Liu, Jia-Quan, Wang, Zhi-Qiang
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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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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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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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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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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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