Results 161 to 170 of about 15,743 (200)

Landesman-lazer conditions and quasilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 1997
The quasilinear elliptic boundary value problem \[ -\Delta_p u=\lambda_1 |u|^{p-2} u+f(x,u)- h\text{ in } \Omega, \quad u=0 \text{ on } \partial\Omega \] is studied, where \(\Omega\subset \mathbb{R}^N\) is a smooth bounded domain, \(p>1\), \(\Delta_p u= \text{div} (|\nabla u|^{p-2} \nabla u)\) is the \(p\)-Laplacian, \(f(x,s)\) is a bounded ...
D. ARCOYA, ORSINA, Luigi
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Oscillation Theorems for Quasilinear Elliptic Differential Equations

Acta Mathematica Sinica, English Series, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Regularity for quasilinear degenerate elliptic equations

Mathematische Zeitschrift, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DI FAZIO, Giuseppe, ZAMBONI, Pietro
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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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Global bifurcation for quasilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 1997
Rabinowitz's global bifurcation theorem has been extended to the equation \[ -\text{div} \bigl(| \nabla u|^{p-2} \nabla u\bigr) =f(\lambda,x,u)\quad \text{in }\Omega, \quad u=0 \quad \text{on } \partial\Omega \] by many authors. In this paper, the left hand side operator is generalized to \(-\text{div} (\varphi(|\nabla u|) \nabla u)\), where \(\varphi ...
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Variational bifurcation for quasilinear elliptic equations

Calculus of Variations and Partial Differential Equations, 2003
The purpose of the paper is to extend Rabinowitz's theorem to a quasi-linear eigenvalue problem of the form \[ \begin{aligned} &(\lambda,u)\in \mathbb R\times H_0^1(\Omega),\\ &\int_\Omega \sum a_{ij}(x,u) D_iuD_jw\,dx+ \tfrac12 \int_\Omega D_sa_{ij}(x,u)D_iu D_jw\,dx- \int_\Omega g(x,u)w\,dx= \lambda\int_\Omega uw\,dw,\\ &\forall w\in H_0^1(\Omega ...
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Quasilinear elliptic equations at critical growth

NoDEA : Nonlinear Differential Equations and Applications, 1998
\noindent The authors study existence of positive functions \(u \in H^1_0(\Omega)\) satisfying (in the distributional sense) the quasilinear elliptic equation \[ -\sum_{i,j = 1}^{N} D_j(a_{ij}(x,u)D_i u) + \frac{1}{2} \sum_{i=1}^{N} \frac{\partial a_{ij}}{\partial s}(x,u) D_i u D_j u = g(x,u) + |u|^{2^{*} - 2} u\quad \text{in }\Omega \] where \(\Omega \
ARIOLI, GIANNI, GAZZOLA, FILIPPO
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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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Solvability of degenerate quasilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 1996
The existence of weak solutions for degenerate elliptic boundary value problems is studied for the equation \[ - \sum^n_{i= 1} {\partial\over \partial x_i} a_i(x, u, \nabla u)+ \nu_0(x)|u|^{p- 2} u+ f(x, u, \nabla u)= 0.\tag{1} \] This equation is a generalization of equations of Klein-Gordon or Schrödinger type.
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Positive solutions for some quasilinear elliptic equations

1996
Summary: Let \(\Omega\) be a bounded open set of \(\mathbb{R}^N\), \(N\geq 1\). We look for solutions of the quasilinear Dirichlet problem \[ u\in H^1_0(\Omega),\quad -\text{div}(A(x,u)Du)= g(x,u), \] where \(A(x,s)\) is a Carathéodory elliptic matrix and \(g(x,s)\) is a Carathéodory function increasing with respect to \(s\).
M. ARTOLA, BOCCARDO, Lucio
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