Results 171 to 180 of about 4,486,095 (208)

Multiple positive solutions for elliptic equations involving a concave term and critical Sobolev–Hardy exponent [PDF]

Applied Mathematics Letters, 2009
In this paper, we establish the existence of multiple positive solutions for elliptic equations involving a concave term and critical Sobolev–Hardy ...
Matallah, A., Bouchekif, M., M. Bouchekif, A. Matallah   +3 more
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-Laplacian problems with critical Sobolev exponents

Nonlinear Analysis: Theory, Methods & Applications, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Perera, Kanishka, Silva, Elves A. B.
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On the p-biharmonic operator with critical Sobolev exponent

Applicationes Mathematicae, 2014
Summary: We study the existence of solutions for a \(p\)-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.
El Khalil, Abdelouahed, Alaoui, My Driss Morchid, Touzani, Abdelfattah   +2 more
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On symmetric solutions of a singular elliptic equation with critical Sobolev–Hardy exponent [PDF]

Journal of Mathematical Analysis and Applications, 2007
This paper is concerned with the existence of the nontrivial solutions of the following problem:{−Δu=μu|x|2+K(x)u2∗(s)−1|x|s,x∈Rn,u∈DG1,2(Rn), where n>2, K(x) is a bounded, continuous function satisfying some conditions.
Yinbin Deng
exaly   +2 more sources

Extrema problems with critical sobolev exponents on unbounded domains

Nonlinear Analysis: Theory, Methods & Applications, 1996
The paper is concerned with the problem of minimizing \(\int_\Omega |\nabla u |^p+a |u |^q\) on the set \(\{u \in {\mathcal D}_0^{1,p} (\Omega):\int_\Omega |u |^{p*}=1\}\).
Ben-Naoum, Abdel Kouider, Troestler, Christophe, Willem, Michel   +2 more
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The Critical Exponent for Weighted Sobolev Imbeddings

Acta Applicandae Mathematica, 2001
The critical exponent \(p^*\) is defined for the Hardy inequality \[ \Biggl(\int^R_0|u(r)|^q Q(r) dr\Biggr)^{1/q}\leq C\Biggl(\int^R_0|u'(r)|^p P(r) dr\Biggr)^{1/p},\tag{2.5} \] defining an imbedding from a weighted Sobolev space \(V\) with weight \(P(r)\) into the weighted Lebesgue space \(L^q(0,R;Q)\) with weight \(Q(r)\), and it is shown that this ...
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Critical exponents of weighted Sobolev embeddings for radial functions

Applied Mathematics Letters, 2020
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Cong Wang 0029, Jiabao Su
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Multiple positive solutions for a semilinear elliptic equation with critical Sobolev exponent [PDF]

Journal of Mathematical Analysis and Applications, 2009
In this paper, we study a class of semilinear elliptic equations with Hardy potential and critical Sobolev exponent. By means of the Ekeland variational principle and Mountain Pass theorem, multiple positive solutions are ...
Haidong Liu
exaly   +2 more sources

The critical Sobolev exponent in two dimensions

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
SynopsisThe object of the paper is to investigate solutions of equations of the formwithand in particular to look at the asymptotic behaviour of these solutions as γ ↑∞. It is found that, if tγ is the first zero of ϑ, thenwhile tγ is bounded below if p < 2.
McLeod, Bryce, McLeod, Kevin
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Quasilinear Elliptic Systems Involving Critical Hardy–Sobolev and Sobolev Exponents

Bulletin of the Malaysian Mathematical Sciences Society, 2015
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Kang, Dongsheng, Kang, Yangguang
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