Results 171 to 180 of about 13,900 (197)

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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Semilinear elliptic equations involving critical Sobolev exponents

Archive for Rational Mechanics and Analysis, 1988
The author considers the semilinear elliptic boundary value problem with variable coefficients: \(Eu=bu^ p+\lambda hu\) in \(\Omega\), \(u>0\) in \(\Omega\) and \(u=0\) on \(\partial \Omega\), where \(Eu\equiv -\partial_ i(a_{ij} \partial_ ju)\) is a symmetric uniformly elliptic operator, b and h are nonnegative nontrivial bounded functions ...
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A minimization problem on RN involving critical Sobolev exponent

Nonlinear Analysis: Theory, Methods & Applications, 1992
The authors develop some technical ideas in order to treat the minimization problem: \[ \inf\left\{\int_{R^ N} a_{ij}(u)D_ i uD_ j u\left| u\in{\mathcal D}^{1,2}(R^ N),\right.\int_{R^ N}| u|^{2^*}=1\right\}, \] where \(2^*=2N/(N-2)\), \(N\geq 3\). By analysing carefully the minimizing sequence, the authors define the corresponding minimization problem ...
Yan, Shusen, Zhang, Zhengjie
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p-Laplacian problems with critical Sobolev exponent

Asymptotic Analysis, 2011
We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical non-linearity in general, possibly non-smooth, bounded domains.
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On Kirchhoff type equations with critical Sobolev exponent

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yisheng Huang, Zeng Liu, Yuanze Wu
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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

Communications on Pure and Applied Mathematics, 1983
Semilinear elliptic equations involving critical Sobolev exponents were considered being hard to attack because of the lack of compactness. Indeed the well known nonexistence results of Pokhožaev asserts that, for a starshaped domain, there is no nontrivial solution for the BVP with critical Sobolev power function as nonlinear term. Surprisingly, it is
Brézis, Haïm, Nirenberg, Louis
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Nonlinear elliptic equations involving critical Sobolev exponents

2000
The purpose of these notes is to present a survey of some recent results dealing with existence, nonexistence and multiplicity of nontrivial solutions for semilinear elliptic equations, whose nonlinear term has critical or supercritical growth.
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Normalized Solutions of the Choquard Equation with Sobolev Critical Exponent

Frontiers of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng, Xiaojing, Li, Yuhua
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On Hamiltonian systems with critical Sobolev exponents

2022
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Multiplicity of positive solutions for a class of critical Sobolev exponent problems involving Kirchhoff-type nonlocal term

Computers and Mathematics With Applications, 2018
Jia-Feng Liao
exaly