In this paper we shall consider the critical elliptic equation -Deltau + lambdaa(x)u = u((N+2)/(N-2)), x is an element of R-N, (0.1) u> 0, integral(R)N \delu\(2)dx < infinity, where lambda > 0, N > 4 and a(x) is a real continuous, non negative function, not identically zero. By using a local Pohozaev identity, we show that problem does not admit a family of solutions u(lambda) which blows-up and concentrates as lambda --> +infinity at some zero point x(0) of a(x) if the order of flatness of the function a(x) at x(0) is beta is an element of [2, N - 4) and N greater than or equal to 7.
Nonexistence of single blow-up solutions for a nonlinear Schrödinger equation involving critical Sobolev exponent
Cingolani, S.;
2004-01-01
Abstract
In this paper we shall consider the critical elliptic equation -Deltau + lambdaa(x)u = u((N+2)/(N-2)), x is an element of R-N, (0.1) u> 0, integral(R)N \delu\(2)dx < infinity, where lambda > 0, N > 4 and a(x) is a real continuous, non negative function, not identically zero. By using a local Pohozaev identity, we show that problem does not admit a family of solutions u(lambda) which blows-up and concentrates as lambda --> +infinity at some zero point x(0) of a(x) if the order of flatness of the function a(x) at x(0) is beta is an element of [2, N - 4) and N greater than or equal to 7.File in questo prodotto:
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