Elliptic equations with nearly critical growth
نویسندگان
چکیده
منابع مشابه
Elliptic Equations with Critical Exponent
where As3 is the Laplace-Beltrami operator on B' . Let 0* C (0, 7r) be the radius o r B ' , i.e., the geodesic distance of the North pole to OBq The values 0 < 0* < 7r/2 correspond to a spherical cap contained in the Northern hemisphere, 0* -7r/2 corresponds to B ~ being the Northern hemisphere and the values rr/2 < 0* < ~c correspond to a spherical cap which covers the Northern hemisphere. Fin...
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has no solution if Ω ⊂ R , N ≥ 3, is bounded and starshaped with respect to some point, and 2∗ = 2N/(N − 2). In (P0) the nonlinear term is a power of u with the critical exponent (N + 2)/(N − 2). This terminology comes from the fact that the continuous Sobolev imbeddings H 0 (Ω) ⊂ L(Ω), for p ≤ 2∗ and Ω bounded, are also compact except when p = 2∗. This loss of compactness reflects in that the ...
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In this paper we deal with the study of limits of solutions of a class of fully nonlinear elliptic problems at nearly critical growth. By means of P.L. Lions’ concentrationcompactness principle, we prove an alternative result for the existence of non-trivial solutions of the limit problem.
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We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (−∆p) u = |u|u in a bounded domain Ω ⊂ R as q approaches the critical Sobolev exponent p∗ = Np/(N − ps). We prove that ground state solutions concentrate at a single point x̄ ∈ Ω and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case p = 2, we prove that for s...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1987
ISSN: 0022-0396
DOI: 10.1016/0022-0396(87)90156-2