Results 31 to 40 of about 4,702,923 (209)

The reaction–diffusion equation with Lewis function and critical Sobolev exponent

, 2002
In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of reaction–diffusion equation with Lewis function and critical Sobolev ...
Tan, Zhong
core   +2 more sources

Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth

Advances in Nonlinear Analysis, 2017
In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
doaj   +1 more source

Existence of nontrivial solutions for biharmonic equations with critical growth

Electronic Journal of Differential Equations
We consider the biharmonic equation with critical Sobolev exponent, $$ \Delta^2u-\Delta u-\Delta(u^2)u+V(x)u=|u|^{2^{**}-2}u+\alpha |u|^{p-2}u,\quad \text{in }\mathbb{R}^N, $$ where $N> 4$, $\alpha>0$, $V(x)$ is a given potential, $2^{**}=\frac{2N}{N-4}$
Juhua He, Ke Wu, Fen Zhou
doaj   +3 more sources

Schrödinger equation with critical Sobolev exponent

Differential and Integral Equations, 2004
In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
openaire   +4 more sources

Existence of positive solutions for Brezis-Nirenberg type problems involving an inverse operator

Electronic Journal of Differential Equations, 2021
This article concerns the existence of positive solutions for the second order equation involving a nonlocal term $$ -\Delta u=\gamma (-\Delta)^{-1} u+|u|^{p-1}u, $$ under Dirichlet boundary conditions.
Pablo Alvarez-Caudevilla, Eduardo Colorado, Alejandro Ortega   +2 more
doaj   +1 more source

Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

Boundary Value Problems, 2021
In this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.
Hongsen Fan, Zhiying Deng
doaj   +1 more source

A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN

Advanced Nonlinear Studies, 2017
This paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:
Xiang Mingqi, Zhang Binlin, Zhang Xia
doaj   +1 more source

A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents [PDF]

Archive for Rational Mechanics and Analysis, 2011
In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents, \label{0.1} {& Δu + λ\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \text{in} Ω, & u=0 \qquad \text{on} Ω, where $0 \le s_2 < s_1 \le 2$, $0 \ne λ\in \Bbb R$ and $0 \in \partial Ω$.
Li, YanYan, Lin, Chang-Shou
openaire   +4 more sources

Resultados de existência para equações elípticas com termos singulares [PDF]

, 2013
Doutoramento em Matemática e AplicaçõesEsta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de equações que envolve o operador Laplaciano, um termo singular e nãolinearidade com o exponente crítico de Sobolev, (II) uma classe de ...
Murillo, Kelly Patricia
core  

High‐Order Projection‐Based Upwind Method for Simulation of Transitional Turbulent Flows

International Journal for Numerical Methods in Fluids, EarlyView.
In this study, we evaluated the implicit large‐eddy simulation capabilities of the mass‐conserving mixed stress method for transitional turbulent flows and proposed an efficient solution method for large‐scale applications. The results presented in this work show promising outcomes for incompressible aerodynamic flow problems, which can be further ...
Philip L. Lederer, Xaver Mooslechner, Joachim Schöberl   +2 more
wiley   +1 more source