146 research outputs found
Continuous selections of solution sets to Volterra integral inclusions in Banach spaces
We consider a nonlinear Volterra integral equation governed by an
m-accretive operator and a multivalued perturbation in a separable Banach.
The existence of a continuous selection for the corresponding solution map
is proved. The case when the m-accretive operator in the integral inclusion
depends on time is also discussed.Universidade de AveiroFCTFEDER POCTI/MAT/55524/200
Positive solutions for parametric nonlinear periodic problems with competing nonlinearities
We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator plus an indefinite potential and a reaction having the competing effects of concave and convex terms. For the superlinear (concave) term we do not employ the usual in such cases Ambrosetti-Rabinowitz condition. Using variational methods together with truncation, perturbation and comparison techniques, we prove a bifurcation-type theorem describing the set of positive solutions as the parameter varies
Periodic problems with a reaction of arbitrary growth
We consider nonlinear periodic equations driven by the scalar p-Laplacian and with a Carath eodory reaction which does not satisfy a global growth condition. Using truncation-perurbation techniques, variational methods and Morse theory, we prove a "three solutions theorem", providing sign information for all the solutions. In the semilinear case (p = 2), we produce a second nodal solution, for a total of four nontrivial solutions. We also cover problems which are resonant at zero
Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and
”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation
and comparison techniques, we show that for all small values of the parameter > 0, the problem
has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert
space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign
Semilinear neumann equations with indefinite and unbounded potential
We consider a semilinear Neumann problem with an indefinite
and unbounded potential, and a Carathéodory reaction term. Under asymptotic conditions on the reaction which make the energy functional coercive,
we prove multiplicity theorems producing three or four solutions with sign
information on them. Our approach combines variational methods based
on the critical point theory with suitable perturbation and truncation techniques, and with Morse theory
Multiple solutions with sign information for (p, 2)−equations with asymmetric resonant reaction
We consider a nonlinear nonhomogeneous Dirichlet problem driven
by the sum of a p−Laplacian and a Laplacian (a (p, 2)− equation). The reaction
is the sum of two competing terms, a parametric (p − 1)−sublinear term and
an asymmetric (p − 1)−linear perturbation which is resonant at −∞. Using
variational methods together with truncations and comparison techniques and
Morse theory (critical groups), we prove two multiplicity theorems which provide
sign information for all the solutions.publishe
Nonlinear Robin problems with locally defined reaction
We consider a nonlinear Robin problem driven by a p− Laplacian.
The reaction consistes of two terms. The first one is parametric and only locally
defined, while the second one is (p − 1)- superlinear. Using cutt-off techniques
together with critical point theory and critical groups, we show that for big values
of the parameter λ > 0, the problem has at least three nontrivial solutions, all
with sign information (positive, negative and nodal). In the semilinear case (p =
2), we produce a second nodal solution, for a total of four nontrivial solutions,
all with sign information.publishe
Positive solutions for parametric nonlinear nonhomogeneous Robin problems
We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. Using variational tools together with suitable truncation and perturbation techniques, we prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter.in publicatio
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations
We consider nonlinear, nonhomogeneous Dirichlet problems driven
by the sum of a p−Laplacian (p > 2) and a Laplacian, with a reaction term
which has space dependent zeros of constant sign. We prove three muliplicity
theorems for such equations providing precise sign information for all solutions.
In the first multiplicity theorem, we do not impose any growth condition on
the reaction near ±∞: In the other two, we assume that the reaction is (p − 1)−
linear and resonant with respect to principal eigenvalue of
(
−△p;W1,p
0 (Ω)
)
: Our
approach uses variational methods based on the critical point theory, together
with suitable truncation and comparison techniques and Morse theory (critical
groups)
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