in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in R. Using this we prove a sharp singular Adams inequality in high order Sobolev spaces in bounded domain at critical case. Then we prove sharp singular Adams inequalities for high order derivatives on unbounded domains. Our results extend...

We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CRpluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions on the sphere, and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolev inequali...

Let Ω ⊂ R4 be a smooth oriented bounded domain, H 2 0 (Ω) be the Sobolev space, and λ(Ω) = inf u∈H 2 0 (Ω),‖u‖2=1 ‖ u‖ 2 2 be the first eigenvalue of the bi-Laplacian operator 2. Then for any α: 0 α < λ(Ω), we have sup u∈H 2 0 (Ω),‖ u‖2=1 ∫ Ω e32π u(1+α‖u‖2) dx <+∞ and the above supremum is infinity when α λ(Ω). This strengthens Adams’ inequality in dimension 4 [D. Adams, A sharp inequality of ...

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...

The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator Gauss space are detected. existence extremal functions relevant is also established. Our results disclose analogies and dissimilarities comparison with Adams' inequality Laplace operator, companion our Euclidean space.