199 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
Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential
We study perturbations of the eigenvalue problem for the negative Laplacian
plus an indefinite and unbounded potential and Robin boundary condition. First
we consider the case of a sublinear perturbation and then of a superlinear
perturbation. For the first case we show that for
( being the principal
eigenvalue) there is one positive solution which is unique under additional
conditions on the perturbation term. For
there are no positive solutions. In the superlinear case, for
we have at least two positive solutions and for
there are no positive solutions. For both
cases we establish the existence of a minimal positive solution
and we investigate the properties of the map
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
Robin problems with indefinite linear part and competition phenomena
We consider a parametric semilinear Robin problem driven by the Laplacian
plus an indefinite potential. The reaction term involves competing
nonlinearities. More precisely, it is the sum of a parametric sublinear
(concave) term and a superlinear (convex) term. The superlinearity is not
expressed via the Ambrosetti-Rabinowitz condition. Instead, a more general
hypothesis is used. We prove a bifurcation-type theorem describing the set of
positive solutions as the parameter varies. We also show the
existence of a minimal positive solution and determine the
monotonicity and continuity properties of the map
Double-phase problems with reaction of arbitrary growth
We consider a parametric nonlinear nonhomogeneous elliptic equation, driven
by the sum of two differential operators having different structure. The
associated energy functional has unbalanced growth and we do not impose any
global growth conditions to the reaction term, whose behavior is prescribed
only near the origin. Using truncation and comparison techniques and Morse
theory, we show that the problem has multiple solutions in the case of high
perturbations. We also show that if a symmetry condition is imposed to the
reaction term, then we can generate a sequence of distinct nodal solutions with
smaller and smaller energies
Nonlinear singular problems with indefinite potential term
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous
differential operator plus an indefinite potential. In the reaction we have the
competing effects of a singular term and of concave and convex nonlinearities.
In this paper the concave term is parametric. We prove a bifurcation-type
theorem describing the changes in the set of positive solutions as the positive
parameter varies. This work continues our research published in
arXiv:2004.12583, where and in the reaction the parametric term
is the singular one.Comment: arXiv admin note: text overlap with arXiv:2004.1258
Positive solutions for nonvariational Robin problems
We study a nonlinear Robin problem driven by the -Laplacian and with a
reaction term depending on the gradient (the convection term). Using the theory
of nonlinear operators of monotone-type and the asymptotic analysis of a
suitable perturbation of the original equation, we show the existence of a
positive smooth solution
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