Results 81 to 90 of about 4,486,095 (208)
Infinitely many positive solutions for p-Laplacian equations with singular and critical growth terms
Boundary Value ProblemsIn 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
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On Dirac equation with a potential and critical Sobolev exponent
Communications on Pure and Applied Analysis, 2015 The authors consider a Dirac equation with a nonlinear zero order term and additional potential on a closed spin manifold. The nonlinearity is critical in the sense of Sobolev embedding -- analogously to the nonlinearity of the Yamabe equation. They prove existence of solutions under some mild assumption on the spectrum of the Dirac operator with ...
Gong, Wenmin, Lu, Guangcun
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Non-homogeneous problem for fractional Laplacian involving critical Sobolev exponent
Electronic Journal of Differential Equations, 2017 In this article, we study the existence of positive solutions for the nonhomogeneous fractional equation involving critical Sobolev exponent $$\displaylines{ (-\Delta)^{s} u +\lambda u=u^p+\mu f(x), \quad u>0\quad \text{in } \Omega,\cr u =0, \quad \
Kun Cheng, Li Wang
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Abstract and Applied Analysis, 2019 In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains.
Mustapha Khiddi
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Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight
Electronic Journal of Differential Equations, 2016 In this article we consider the problem $$\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 }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$, We study ...
Mohammed Bouchekif, Ali Rimouche
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Existence of nontrivial solutions for biharmonic equations with critical growth
Electronic Journal of Differential EquationsWe consider the biharmonic equation with critical Sobolev exponent, $$ \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, $$ where $N> 4$, $\alpha>0$, $V(x)$ is a given potential, $2^{**}=\frac{2N}{N-4}$
Juhua He, Ke Wu, Fen Zhou
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Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality [PDF]
, 2008 9 pages, no figures.-- MSC2000 code: 33C45.MR#: MR2431543 (2009g:41009)Zbl#: Zbl 1155.33006We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same $n ...
Díaz Mendoza, Carlos J. +3 more
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Existence of solutions for elliptic systems with critical Sobolev exponent
Electronic Journal of Differential Equations, 2002 We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
Pablo Amster +2 more
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Two positive solutions for quasilinear elliptic equations with singularity and critical exponents
Boundary Value Problems, 2018 In this paper, we consider the quasilinear elliptic equation with singularity and critical exponents {−Δpu−μ|u|p−2u|x|p=Q(x)|u|p∗(t)−2u|x|t+λu−s,in Ω,u>0,in Ω,u=0,on ∂Ω, $$ \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 existence of extremals for the Sobolev trace embedding theorem with critical exponent
, 2005 In this paper, the existence problem is studied for extremals of the Sobolev trace inequality W-1,W-p(Omega) --> L-p* (partial derivativeOmega), where Omega is a bounded smooth domain in R-N, p(*) = p(N - 1)/(N - p) is the critical Sobolev exponent, and ...
Bonder, JF, Rossi, JD
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