Results 61 to 70 of about 208 (138)

A singular ODE related to quasilinear elliptic equations

Electronic Journal of Differential Equations, 2000
We consider a quasilinear elliptic problem with the natural growth in the gradient. Existence, non-existence, uniqueness, and qualitative properties of positive solutions are obtained. We consider both weak and strong solutions.
Luka Korkut, Mervan Pasic, Darko Zubrinic   +2 more
doaj  

Norm Comparison Estimates for the Composite Operator

Journal of Function Spaces, 2014
This paper obtains the Lipschitz and BMO norm estimates for the composite operator 𝕄s∘P applied to differential forms. Here, 𝕄s is the Hardy-Littlewood maximal operator, and P is the potential operator.
Xuexin Li, Yong Wang, Yuming Xing
doaj   +1 more source

Quasilinear Differential Constraints for Parabolic Systems of Jordan‐Block Type

Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.
ABSTRACT We prove that linear degeneracy is a necessary conditions for systems in Jordan‐block form to admit a compatible quasilinear differential constraint. Such condition is also sufficient for 2×2$2\times 2$ systems and turns out to be equivalent to the Hamiltonian property.
Alessandra Rizzo, Pierandrea Vergallo
wiley   +1 more source

A Degenerate Neumann Problem for Quasilinear Elliptic Equations

Tokyo Journal of Mathematics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Taira, K., Palagachev, D. K., Popivanov, P. R.   +2 more
openaire   +3 more sources

Quasilinear elliptic problems with nonstandard growth

Electronic Journal of Differential Equations, 2011
We prove the existence of solutions to Dirichlet problems associated with the $p(x)$-quasilinear elliptic equation $$ Au =- hbox{div} a(x,u,abla u)= f(x,u,abla u). $$ These solutions are obtained in Sobolev spaces with variable exponents.
Mohamed Badr Benboubker, Elhoussine Azroul, Abdelkrim Barbara   +2 more
doaj  

Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁

International Journal of Differential Equations, 2010
Assume that 𝑄 is a positive continuous function in ℝ𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation −Δ𝑝𝑢+|𝑢|𝑝−2𝑢=𝑄(𝑧)|𝑢|𝑞−2𝑢 in ℝ𝑁 admits at least two solutions in ℝ𝑁 (one is a positive ground-state solution and ...
Huei-li Lin
doaj   +1 more source

Quasilinear degenerate elliptic equation with absorption term

Nonlinear Analysis: Theory, Methods & Applications, 1999
The author studies the Dirichlet problem for \(p\)-harmonic operators \[ L_pu=-\text{div} (A(x)|\nabla u|^{p-2}\nabla u) \] with absorption term \[ L_pu+B(x)Q(u)= f(x)\quad \text{in } \Omega,\qquad u=0\quad \text{on } \partial\Omega. \] Here \(B(x)\) is a nonnegative function on \(\Omega\) and \(Q(t)\) is a continuous and strictly monotone increasing ...
openaire   +3 more sources

Generating Singularities of Solutions of Quasilinear Elliptic Equations

Journal of Mathematical Analysis and Applications, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Local renormalized solutions of elliptic equations with variable exponents in unbounded domains

Современная математика: Фундаментальные направления
In this paper, we consider a second-order quasilinear elliptic equation with variable nonlinearity exponents and a locally summable right-hand side.
L. M. Kozhevnikova
doaj   +1 more source

Eigenvalue problems for a quasilinear elliptic equation on ℝN

International Journal of Mathematics and Mathematical Sciences, 2005
We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x)|u|p−2u, x∈ℝN, lim|x|→+∞u(x)=0, where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator and the weight function g(x), being bounded ...
Marilena N. Poulou, Nikolaos M. Stavrakakis   +1 more
doaj   +1 more source