4,743 research outputs found
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution
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
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
Existence and Relaxation Results for Second Order Multivalued Systems
We consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term A(x) and of a multivalued perturbation F(t, x, y) which can be convex or nonconvex valued. We consider the cases where D(A) ≠ RN and D(A) = RN and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed
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
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
Comparison of resin modified glass ionomer cement and composite resin in class II primary molar restorations: a 2-year parallel randomised clinical trial
AIM
To compare the 2-year success rates of a Resin Modified Glass Ionomer Cement (RMGIC) with a composite resin in class II primary molar restorations.
METHODS
Healthy, cooperative children aged 4-7.5 years with at least one carious primary molar requiring a class II restoration were included in this parallel randomised trial and allocated on a 1:1 basis to composite resin (Z250, 3M ESPE) or RMGIC (Vitremer, 3M ESPE). Restorations were assessed semiannually up to 2 years clinically and radiographically using modified United States Public Health Service criteria, with the primary outcome being all-cause failure. Data were analysed per protocol by binomial linear regression with Relative Risks (RR) and their 95% confidence intervals (CI).
RESULTS
55 patients were randomly allocated to either group and 44 analysed at 2 years; with 49 teeth in the Z250 and 55 teeth in the Vitremer group. The all-cause failure rate for both materials was 3% after 1 year (4 and 2% for Z250 and Vitremer, respectively) and 16% after 2 years (16% for both Z250 and Vitremer). Overall, no difference between materials could be found at 2 years (RR = 1.4; 95% CI 0.8, 2.4; P = 0.30). However, Vitremer was associated with more favourable gingival health compared to composite (RR = 0.2; 95% CI 0.1, 0.9; P = 0.03), but also occlusal wear, which was observed exclusively for Vitremer.
CONCLUSION
No significant difference was found in the overall performance of the two materials, making them suitable for class II primary molar restorations, although RMGIC presented more pronounced occlusal wear of limited clinical importance after 2 years
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
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