Results 21 to 30 of about 410 (182)

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

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.
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Existence Results for Singular p-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent

Axioms
In this article, we consider the singular p-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold ...
Gurpreet Singh
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A singular perturbed problem with critical Sobolev exponent

Topological Methods in Nonlinear Analysis, 2021
This paper deals with the following nonlinear elliptic problem \begin{equation}\label{eq0.1} -\varepsilon^2\Delta u+\omega V(x)u=u^{p}+u^{2^{*}-1},\quad u> 0\quad\text{in}\ \R^N, \end{equation} where $\omega\in\R^{+}$, $N\geq 3$, $p\in (1,2^{*}-1)$ with $2^{*}={2N}/({N-2})$, $\varepsilon> 0$ is a small parameter and $V(x)$ is a given function ...
Mengyao Chen, Qi Li
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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
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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
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

Advances in Nonlinear Analysis, 2020
We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
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Stability of Viscous Three‐Dimensional Stratified Couette Flow via Dispersion and Mixing

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT This article explores the stability of stratified Couette flow in the viscous 3d$3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves.
Michele Coti Zelati, Augusto Del Zotto, Klaus Widmayer   +2 more
wiley   +1 more source

Strongly indefinite systems with critical Sobolev exponents [PDF]

Transactions of the American Mathematical Society, 1998
We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.
MITIDIERI, ENZO, HULSHOF J, VAN DER VORST R.   +2 more
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Solvability and Boundedness in Chemotaxis‐Consumption Models With Oppositely Acting Nonlocal Sources

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we investigate a chemotaxis system featuring a class of external source terms that incorporate both local and nonlocal growth as well as dampening effects. The model describes the evolution of a cell density u$$ u $$, which migrates in response to a chemical signal v$$ v $$, within an impermeable habitat.
Rafael Díaz Fuentes, Fatma Gamze Düzgün, Silvia Frassu, Giuseppe Viglialoro   +3 more
wiley   +1 more source