1,721,002 research outputs found
Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth
No full textBy combining a technique inspired to the theory of sublinear elliptic equations with the Emden-Fowler inversion technique of Atkinson and Peletier, we obtain uniqueness of positive solutions of the following equation -Δu = λueu θ in B, u > 0, u = 0 on ∂B, where B ⊂ Rn is the ball of radius one, λ > 0 and 1 < ν ≤ 2
On the existence and radial symmetry of maximizers for functionals with critical exponential growth in R^2
No full textPerturbation of symmetry and multiplicity of solutions for strongly indefinite elliptic systems
No full textWe consider the following elliptic system:
-\Delta u= |v|^{p-1} v + h(x) %
& x\in \Omega \\
-\Delta v= |u|^{q-1} u + k(x) %
& x\in \Omega \\
u=v=0 & x\in \partial \Omega
where \Omega \subset R^N, N\geq 3 is a smooth bounded domain. If h(x)= k(x)= 0 the system presents a natural Z_2 symmetry, which guarantees the existence of infinitely many solutions. In this paper we show that the multiplicity structure can be maintained if (p,q)lies below a suitable curve in R^2
Perturbation from symmetry and multiplicity of solutions for elliptic problems with subcritical exponential growth in R^2
No full textWe consider the following boundary value problem {-Δu = g(x, u) + f(x, u) x ∈ Ω u = 0 x ∈ ∂Ω where g(x, -ξ) = -g(x,ξ) and g has subcritical exponential growth in R2. Using the method developed by Bolle, we prove that this problem has infinitely many solutions under suitable conditions on the growth of g(u) and f(u)
Adams' inequality and limiting Sobolev embeddings into Zygmund spaces
No full textWe exhibit sharp embedding constants for Sobolev spaces of any order into
Zygmund spaces, obtained as the product of sharp embedding constants for second
order Sobolev space into Lorentz spaces. As a consequence, we derive a new proof
of Adams’ inequality, which holds in the larger hypotheses of homogenoeous Navier
boundary contidions
On Trudinger–Moser type inequalities involving Sobolev–Lorentz spaces
Full text linkGeneralizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these
spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between
the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are
related phenomena of concentration-compactness
Erratum: Multiple solutions for quasilinear elliptic problems in R2 with exponential growth
No full textErratum: Multiple solutions for quasilinear elliptic problems in R2 with exponential growt
Multiple solutions of a Kirchhoff type elliptic problem with the Trudinger-Moser growth
No full textWe consider a Kirchhoff type elliptic problem;
{-(1 + alpha integral(Omega) vertical bar del u vertical bar(2)dx) Delta u = f(x, u), u >= 0 in Omega,
u = 0 on partial derivative Omega,
where Omega subset of R-2 is a bounded domain with a smooth boundary partial derivative Omega, alpha > 0 and f is a continuous function in (Omega) over bar x R. Moreover, we assume f has the Trudinger-Moser growth. We prove the existence of solutions of (P), so extending a former result by de Figueiredo-Miyagaki-Ruf [11] for the case alpha = 0 to the case alpha > 0. We emphasize that we also show a new multiplicity result induced by the nonlocal dependence. In order to prove this, we carefully discuss the geometry of the associated energy functional and the concentration compactness analysis for the critical case
Trudinger-type inequalities in with radial increasing mass-weight
No full textWe prove Trudinger type inequalities with radial increasing massweights in the whole RN , in the setting of mass-weighted Sobolev spaces W 1,N w (RN ). Due to the presence of increasing weights, we will not apply symmetrization tools: the proofs of our inequalities mainly rely on a proper transformation of variables, which allows us to reduce the weighted case to the
un-weighted classical one
A Moser-type inequality in Lorentz-Sobolev spaces for unbounded domains in RN
No full textWe derive a Pohoaev-Trudinger type embedding for the Lorentz-Sobolev space W1"0LN,q(Ω), for general domains Ω⊆RN and in particular for Ω=RN. Precisely, we first prove that the corresponding inequality is domain independent and then, by constructing explicit concentrating sequences à la Moser, we establish that the embedding inequality is sharp and we exhibit the best constant
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