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In this paper, we show that the minimizing problem (1) Λ s , α = inf u ∈ H s ( R N ) , u ≢ 0 ∫ R N | ( − Δ ) s 2 u ( x ) | 2 d x ( ∫ R N | u ( x ) | 2 s , α ∗ | x | α d x ) 2 2 s , α ∗ is achieved by a positive, radially symmetric and strictly decreasing function provided 0 s N 2 , 0 α 2 s .

In this paper, we investigate the existence of multiple solutions for critical inhomogeneous elliptic problem in non-contractible domains. We show that for f epsilon H(-1) satisfying a suitable condition and 0

In this paper, we consider semilinear elliptic systems with both singular and critical growth terms in bounded domains. The existence of a nontrivial solution is obtained by variational methods. (C) 2007 Elsevier Ltd. All rights reserved.

In this paper, we consider the existence of multiple positive solutions for an inhomogeneous critical semilinear elliptic problem. We show that the problem possesses at least four positive solutions. (C) 2007 Elsevier Ltd. All rights reserved.

In this paper we study the existence of positive solutions of an inhomogeneous semilinear elliptic equation. Allowing the inhomogeneous term f (x) to change sign, that is, f is an element of C-1(Omega/{0}), we show under further assumptions that the problem has exact one or two positive solutions according to the classification of f. (C) 2004 Elsevier Ltd. All rights reserved.