Results 161 to 170 of about 410 (182)
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ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT
Bulletin of the London Mathematical Society, 2005Summary: In this paper, the existence problem is studied for extremals of the Sobolev trace inequality \(W^{1,p}(\Omega)\hookrightarrow L^{p^*}(\partial\Omega)\), where \(\Omega\) is a bounded smooth domain in \(\mathbb R^N\), \(p^*=p(N-1)/(N-p)\), is the critical Sobolev exponent, and \(1< p < N\).
Bonder, JF, Rossi, JD
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The Neumann Problem for Semilinear Elliptic Equations with Critical Sobolev Exponent
Milan Journal of Mathematics, 2007In this survey article we discuss the existence and the properties of least energy solutions of a semilinear critical Neumann problem. The main focus is on the joint effect of the shape of the graph of coefficients of the critical nonlinearities and the geometry of the boundary on the existence of solutions.
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On some quasilinear elliptic problems involving critical Sobolev exponents
Funkcialaj Ekvacioj, 1993The author studies the existence of a nontrivial radially symmetric solution of the problem \[ -\text{div} \bigl( | \nabla u |^{p- 2} \nabla u \bigr) - Q(x) | u |^{p-2} u-K(x) | u |^{p^*-2} u=0,\text{ in } B_ R,\;u=0 \text{ on } \partial B_ R, \tag{1} \] where \(B_ R\) is the closed ball in \(\mathbb{R}^ n\) with center zero and radius \(R\). The basic
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Fractional Kirchhoff-type equation with Hardy–Littlewood–Sobolev critical exponent
Computers and Mathematics With Applications, 2019Yu Su
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On symmetric solutions of a singular elliptic equation with critical Sobolev–Hardy exponent
Journal of Mathematical Analysis and Applications, 2007Yinbin Deng
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Multiplicity of solutions for a class of elliptic systems with critical Sobolev exponent
Nonlinear Analysis: Theory, Methods & Applications, 2010Yanqin Fang
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Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent
Journal of Mathematical Analysis and Applications, 2010Tiexiang Li, Tsung-Fang Wu
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On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent
Nonlinear Analysis: Theory, Methods & Applications, 2003François Ebobisse
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