Results 81 to 90 of about 406 (185)

Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight

Electronic Journal of Differential Equations, 2016
In this article we consider the problem $$\displaylines{ -\hbox{div}\big(p(x)\nabla u\big)=|u|^{2^{*}-2}u+\lambda f\quad \text{in }\Omega \cr u=0 \quad \text{on }\partial\Omega }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$, We study ...
Mohammed Bouchekif, Ali Rimouche
doaj  

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
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Existence of solutions for elliptic systems with critical Sobolev exponent

Electronic Journal of Differential Equations, 2002
We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
Pablo Amster, Pablo De Napoli, Maria Cristina Mariani   +2 more
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Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

Boundary Value Problems, 2018
In this paper, we consider the quasilinear elliptic equation with singularity and critical exponents {−Δpu−μ|u|p−2u|x|p=Q(x)|u|p∗(t)−2u|x|t+λu−s,in Ω,u>0,in Ω,u=0,on ∂Ω, $$ \textstyle\begin{cases} -\Delta_{p}u-\mu \frac{ \vert u \vert ^{p-2}u}{ \vert x ...
Yanbin Sang, Xiaorong Luo, Zongyuan Zhu
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On the location of the peaks of least-energy solutions to semilinear Dirichlet problems with critical growth

Abstract and Applied Analysis, 2002
We study the location of the peaks of solution for the critical growth problem −ε 2Δu+u=f(u)+u 2*−1, u>0 in Ω, u=0 on ∂Ω, where Ω is a bounded domain; 2*=2N/(N−2), N≥3, is the critical Sobolev exponent and f has a behavior like up ...
Marco A. S. Souto
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Existence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity

Fractal and Fractional
We consider a Neumann problem for the fractional Laplacian involving a nonlocal Choquard-type nonlinearity and Sobolev–Hardy exponent. Under suitable assumptions on the data and using the Nehari manifold method, we discuss the existence problem in ...
Zhenfeng Zhang, Calogero Vetro, Tianqing An, Wei Chen   +3 more
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Existence of solutions for Choquard equations with an L 1 $L^{1}$ -integrable reciprocal potential and upper critical growth

Boundary Value Problems
This paper is dedicated to studying the Choquard-type equation { − Δ u + V ( x ) u = ( I α ∗ | u | p ) | u | p − 2 u + λ | u | q − 2 u , u ∈ H 1 ( R N ) , $$ \left \{ \textstyle\begin{array}{l} - \Delta u + V(x)u = ( {{I_{\alpha }} * {{\left | u \right |}
Ting Guo, Tianle Xia, Xianhua Tang
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The Existence of Positive Solution for Semilinear Elliptic Equations with Multiple an Inverse Square Potential and Hardy-Sobolev Critical Exponents

Abstract and Applied Analysis, 2019
Via the concentration compactness principle, delicate energy estimates, the strong maximum principle, and the Mountain Pass lemma, the existence of positive solutions for a nonlinear PDE with multi-singular inverse square potentials and critical Sobolev ...
M. Khiddi
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Regression in tensor product spaces by the method of sieves. [PDF]

Electron J Stat, 2023
Zhang T, Simon N.
europepmc   +1 more source

Multiplicity of solutions to the sum of polyharmonic equations with critical Sobolev exponents

Electronic Journal of Differential Equations, 2015
In this article, we prove multiplicity of solutions for the sum of polyharmonic equation with critical Sobolev exponent. The proof is based upon the methods of weakly lower semi-continuous of the functionals and the Mountain Pass Lemma without (PS ...
Wei Liu, Gao Jia, Lu-Quian Guo
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