Results 241 to 250 of about 89,789 (287)

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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Harnack Inequality for Quasilinear Elliptic Equations in Generalized Orlicz-Sobolev Spaces

Potential Analysis, 2020
Allami Benyaiche, Ismail Khlifi
semanticscholar   +1 more source

Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces

Positivity (Dordrecht), 2020
Allami Benyaiche, Ismail Khlifi
semanticscholar   +1 more source

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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Multiple solutions for quasilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 1990
The author uses degree theory for mappings of class \((S)_+\) [see \textit{F. E. Browder}, Bull. Am. Math. Soc., New Ser. 9, 1-39 (1983; Zbl 0533.47053)] to determine the existence of multiple weak solutions to boundary value problems of the form \(Au-g(u)=0\) in \(\Omega \subset {\mathbb{R}}^ N\), \(u=0\) on \(\partial \Omega\), where \(\Omega\) is a ...
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A Strong Maximum Principle for some quasilinear elliptic equations

, 1984
J. Vázquez
semanticscholar   +1 more source

Colloidal Self-Assembly Approaches to Smart Nanostructured Materials

Chemical Reviews, 2022
Zhiwei Li Li, Yadong Yin
exaly