Results 61 to 70 of about 1,238 (226)

Sign Changing Solutions for Coupled Critical Elliptic Equations

Journal of Function Spaces, 2020
In this paper, we consider the coupled elliptic system with a Sobolev critical exponent.
Xin Wang, Xiaorui Yue
doaj   +1 more source

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley   +1 more source

On Elliptic System Involving Critical Sobolev–Hardy Exponents

Mediterranean Journal of Mathematics, 2008
This paper deals with a class of nonlinear elliptic system involving Sobolev-Hardy exponents in bounded domain of \({\mathbb{R}}^{N}\). By using variational method, we show that the existence of solutions depend on certain parameters.
Mohammed Bouchekif, Yasmina Nasri
openaire   +3 more sources

Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang, Xueqi Sun, Shuaishuai Liang, Vicenţiu D. Rădulescu   +3 more
wiley   +1 more source

Element‐Based Internal Variable Formulations for Finite Element Discretizations in FFT‐Based Homogenization Methods

International Journal for Numerical Methods in Engineering, Volume 126, Issue 21, 15 November 2025.
ABSTRACT Although finite elements were made available for FFT‐based computational homogenization methods, they are seldomly used for inelastic computations because traditionally the constitutive law is evaluated at each quadrature point of the element, making the storage of that many internal variables necessary, as well.
Flavia Gehrig, Matti Schneider
wiley   +1 more source

Existence results for elliptic systems involving critical Sobolev exponents

Electronic Journal of Differential Equations, 2004
n this paper, we study the existence and nonexistence of positive solutions of an elliptic system involving critical Sobolev exponent perturbed by a weakly coupled term.
Mohammed Bouchekif, Yasmina Nasri
doaj  

A note on problems involving critical Sobolev exponents

Differential and Integral Equations, 1995
Existence of a nontrivial solution of the semilinear elliptic equation \(- \Delta u= | u|^{p-2} u+ f(x,u)\) in \(G\), \(u=0\) on \(\partial G\) is shown in this paper. Here \(G\) denotes a smooth bounded domain in \(\mathbb{R}^ N\) \((N\geq 4)\), \(p-1= (N+2)/ (N-2)\) (the so-called critical Sobolev exponent) and \(f(x,u)= \lambda u+ g(x,u)\) is ...
Costa, D. G., Silva, E. A.
openaire   +3 more sources

The Numbers of Positive Solutions by the Lusternik-Schnirelmann Category for a Quasilinear Elliptic System Critical with Hardy Terms

Abstract and Applied Analysis, 2019
In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains.
Mustapha Khiddi
doaj   +1 more source

Infinitely many positive solutions for p-Laplacian equations with singular and critical growth terms

Boundary Value Problems
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p-Laplacian type involving a singularity and a critical Sobolev exponent { − Δ p u = u p ∗ − 1 + λ | u | γ − 1 u , in Ω , u = 0 , on ∂ Ω ...
Chen-Xi Wang, Hong-Min Suo
doaj   +1 more source