81 research outputs found
Combined effects for non-autonomous singular biharmonic problems
We study the existence of nontrivial weak solutions for a class of
generalized -biharmonic equations with singular nonlinearity and Navier
boundary condition. The proofs combine variational and topological arguments.
The approach developed in this paper allows for the treatment of several
classes of singular biharmonic problems with variable growth arising in applied
sciences, including the capillarity equation and the mean curvature problem
Yamabe-type equations on Carnot groups
This article is concerned with a class of elliptic equations on Carnot groups
depending of one real positive parameter and involving a critical nonlinearity.
As a special case of our results we prove the existence of at least one
nontrivial solution for a subelliptic critical equation defined on a smooth and
bounded domain of the {Heisenberg group} . Our approach is based on pure variational methods and locally
sequentially weakly lower semicontinuous arguments
On nerves of fine coverings of acyclic spaces
The main results of this paper are: (1) If a space can be embedded as a
cellular subspace of then admits arbitrary fine open
coverings whose nerves are homeomorphic to the -dimensional cube
; (2) Every -dimensional cell-like compactum can be embedded
into -dimensional Euclidean space as a cellular subset; and (3) There
exists a locally compact planar set which is acyclic with respect to \v{C}ech
homology and whose fine coverings are all nonacyclic
Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness
We study the following Kirchhoff equation A
special feature of this paper is that the nonlinearity and the potential
are indefinite, hence sign-changing. Under some appropriate assumptions on
and , we prove the existence of two different solutions of the equation
via the Ekeland variational principle and Mountain Pass Theorem
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