1,721,010 research outputs found
Variational properties of the first curve of the Fučík spectrum for elliptic operators
Full text linkIn this paper we present a new variational characteriztion of the
first nontrival curve of the Fucik spectrum for elliptic
operators with Dirichlet boundary conditions.
Moreover, we describe the asymptotic behaviour and some properties of
this curve and of the corresponding eigenfunctions.
In particular, this new characterization allows us to compare the
first curve of the Fucik spectrum with the infinitely many
curves we obtained in previous works; for example,
we show that these curves are all asymptotic to the same lines as the
first curve, but they are all distinct from such a curve
Nonlinear elliptic Dirichlet problems in exterior domains: the role of geometry and topology of the domain
No full textInfinitely many solutions for elliptic equations with non-symmetric nonlinearities
No full textWe deal with the existence of infinitely many solutions for a class of elliptic problems with non-symmetric nonlinearities. Our result, which is motivated by a well known conjecture formulated by A. Bahri and P.L. Lions, suggests a new approach to tackle these problems. The proof is based on a method which does not require to use techniques of deformation from the symmetry and may be applied to more general non-symmetric problems
Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains
No full textWe deal with nonlinear elliptic Dirichlet problems of the form
where is a bounded domain in , , p> 1 and
has supercritical growth from the viewpoint of Sobolev embedding.
o Our aim is to show that there exist bounded contractible non
star-shaped domains , arbitrarily close to domains with
nontrivial topology, such that the problem does not have nontrivial
solutions.
For example, we prove that if , 1<2, with
q>{2pover 2-p} and Omega={(
hocos heta,
hosin heta) :
| heta|{2pover 2-p} there exists ar s>0 such that the
problem has only the trivial solution for all and
Uniqueness of solutions for nonlinear dirichlet problems with supercritical growth
No full textWe are concerned with Dirichlet problems of the form div(|Du|p-2Du)+f (u)=0 in Ω, u=0 on ∂Ω, where Ω is a bounded domain of Rn, n≥2, 10 small enough, Ωε,s={(x1, x2) ∈ R2: Dist ((x1, x2), Γ) I2 and Ω is, for example, a domain of the type Ω=Ωε,s ={(x1,x2,y):(x1,x2)∈ΩΓε, y∈Rn-2, |y
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