Results 111 to 120 of about 14,416 (203)

Entire solutions of quasilinear elliptic equations

Journal of Mathematical Analysis and Applications, 2009
The author studies the entire solutions of non-homogeneous quasilinear elliptic equations for which the following two may serve as typical examples: \[ \begin{aligned} \Delta_pu\equiv \text{div}(|Du|^{p-2}Du) &=f(u), \quad p>1,\;x\in\mathbb R^n, \tag{1}\\ \text{div}\left(\frac{Du}{\sqrt{1+|Du|^2}}\right) &=f(u), \quad x\in\mathbb R^n.
openaire   +2 more sources

The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion. [PDF]

Arch Ration Mech Anal, 2022
Disconzi MM, Ifrim M, Tataru D.
europepmc   +1 more source

Entire radial bounded solutions for Leray-Lions equations of (p, q)-type

Advances in Nonlinear Analysis
We prove the existence of entire, radial, and signed bounded solutions for a quasilinear elliptic equation in RN{{\mathbb{R}}}^{N} driven by a Leray-Lions operator of the (p, q)-type.
Mennuni Federica, Mugnai Dimitri, Salvatore Addolorata   +2 more
doaj   +1 more source

Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]

Calc Var Partial Differ Equ, 2021
Bögelein V, Heran A, Schätzler L, Singer T.   +3 more
europepmc   +1 more source

Statistical finite elements for misspecified models. [PDF]

Proc Natl Acad Sci U S A, 2021
Duffin C, Cripps E, Stemler T, Girolami M.   +3 more
europepmc   +1 more source

Unique continuation for solutions of p(x)-Laplacian equations

Electronic Journal of Differential Equations, 2012
We study the unique continuation property for solutions to the quasilinear elliptic equation $$ hbox{div}(|abla u|^{p(x)-2}abla u) +V(x)|u|^{p(x)-2}u=0quad hbox{in }Omega, $$ where $Omega$ is a smooth bounded domain in $mathbb{R}^N$ and $1<p(x)&
Johnny Cuadro, Gabriel Lopez G.
doaj  

Nontrivial solutions for resonance quasilinear elliptic systems

Advances in Nonlinear Analysis
We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically (p,q)\left(p,q)-linear at infinity.
Borgia Natalino, Cingolani Silvia, Vannella Giuseppina   +2 more
doaj   +1 more source

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS WITH ADVANCED GLYCATION END-PRODUCTS. [PDF]

Appl Anal, 2022
Xie X.
europepmc   +1 more source

Asymptotics for some quasilinear elliptic equations

Differential and Integral Equations, 1996
Let $B$ be the unit ball of $\mathbb{R}^n$, $n \ge 3$. We consider the problem $\Delta u = f(\vert x\vert)u^{p-\epsilon}$ in $B$, $u > 0$ in $B$, $u = 0$ on $\partial B$, where $f \in C^\infty(\mathbb{R},\mathbb{R})$, $p = (n+2)/(n-2)$, $\epsilon \ge 0$.
openaire   +4 more sources

Optimal $C^{1, \alpha}$ regularity for quasilinear elliptic equations with Orlicz growth

Electronic Journal of Qualitative Theory of Differential Equations
In this paper we obtain the interior optimal $C^{1, \alpha}$ regularity of weak solutions for the following quasilinear elliptic equations with Orlicz growth in divergence form \begin{equation*} -\operatorname{div}a(x, Du)=- \operatorname{div} \textbf{F}
Xiaohan Wang, Fengping Yao
doaj   +1 more source