Results 191 to 200 of about 16,559 (211)

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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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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On a jumping problem for quasilinear elliptic equations

Mathematische Zeitschrift, 1997
In a simply connected region \(\Omega\subset\mathbb{R}^n(n\geq 3)\) the boundary problem \[ \begin{aligned} &L(x,u,Du)=-\sum^n_{i,j=1} D_j\bigl(a_{ij} (x,u)D_i u\bigr) +{1 \over 2}\sum^n_{i,j=1} D_sa_{ij}(x,u) D_iuD_ju =g(x,u)+ \omega,\\ & u=0 \text{ on }\partial \Omega\end{aligned} \] is considered, where \(\omega\in H^{-1}(\Omega)\); \[ \begin ...
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Oscillation criteria for quasilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yūki Naito, Hiroyuki Usami
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Unilateral problems for quasilinear elliptic equations

Lithuanian Mathematical Journal, 1982
Translation from Litov. Mat. Sb. 21, No.4, 83-96 (Russian) (1981; Zbl 0485.35044).
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A quasilinear elliptic equation with small parameter [PDF]

Mathematical Notes of the Academy of Sciences of the USSR, 1985
Let u(x,y,\(\epsilon)\) be \(2\pi\)-periodic in y solution of the singularly perturbed problem \[ \epsilon \Delta u+\partial u/\partial x+(\partial u/\partial y)^ 2=0;\quad u|_{x=0}=\phi_ 0(y),\quad u|_{x=1}=\phi_ 1(y), \] where \(\phi_ 0(y)\) and \(\phi_ 1(y)\) are \(2\pi\)-periodic and \(0\leq x\leq 1\).
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A strongly degenerate quasilinear elliptic equation

Nonlinear Analysis: Theory, Methods & Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fuensanta Andreu, José M. Mazón, Vicent Caselles   +2 more
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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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Regularity for quasilinear degenerate elliptic equations

Mathematische Zeitschrift, 2006
Equations like (1.1) have been studied by many Authors in the case ω(x) ≡ 1 (see e.g. [2] and the references therein) or ω an A2 Muckenhoupt weight ([6] and [17]). Here 3 is a strong A∞ weight and ω = 31− p n , 1 < p < n. The novelty here is the degeneracy condition given by choice of the weight ω to be a power of a strong A∞ weight.
DI FAZIO, Giuseppe, ZAMBONI, Pietro
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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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