Search results for "Solutions"
showing 10 items of 757 documents
Lower semicontinuity of weak supersolutions to the porous medium equation
2013
Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. This shows that weak supersolutions belong to a class of supersolutions defined by a comparison principle.
Electrochemical corrosion assessment of RaCe and Mtwo rotary nickle-titanium instruments after clinical use and sterilization
2010
Aim: The aim of the present study was to electrochemically evaluate corrosion resistance of RaCe and Mtwo files after repeated sterilization and preparation procedures. Study Design: A total of 450 rotary files were used. In the working groups, 72 files from each file type were distributed into 4 groups. RaCe and Mtwo files were used to prepare one root canal of the mesial root of extracted human mandibular first molars. The procedure was repeated to prepare 2 to 8 canals. The following irrigation solutions were used: group 1, RaCe files with 2.5% NaOCl; group 2, RaCe files with normal saline; group 3, Mtwo files with 2.5% NaOCl; and group 4, Mtwo files with normal saline in the manner desc…
Direct injection of edible oils as microemulsions in a micellar mobile phase applied to the liquid chromatographic determination of synthetic antioxi…
1999
Abstract A simple and quick procedure for analysis of hydrophobic samples by direct injection in a liquid chromatograph, without previous extraction, has been developed. The sample is solved in a water/sodium dodecyl sulphate/n-pentanol microemulsion without destroying the microemulsion structure, and injected. A micellar mobile phase containing 0.1 M SDS, 2.5% n-propanol and 10 mM phosphate of pH 3 is used. The procedure is applied to the determination of synthetic antioxidants (propyl gallate, tert-butylhydroquinone, 2,4,5-trihydroxybutyrophenone, nordihydroguaiaretic acid, octyl gallate, 3-tert-butyl-4-hydroxyanisole and dodecyl gallate) in sunflower, corn and olive oils. Linear calibrat…
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.
An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations
2020
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.
On critical behaviour in generalized Kadomtsev-Petviashvili equations
2016
International audience; An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev–Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the disp…
Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering
2017
Abstract The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.
Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator
2020
Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.
Branches of index-preserving solutions to systems of second order ODEs
2009
We investigate the existence of a continuum of index-preserving solutions to a Dirichlet problem associated with a parameter-dependent system of second order ordinary differential equations, developing a detailed analysis on the behaviour of the branches of nontrivial solutions. Our approach is based on the Rabinowitz global bifurcation Theorem combined with the notion of index and nullity of suitable linear boundary value problems. An application of the result to the study of branches of odd, periodic solutions for suitable systems of two linearly coupled pendulums of lenghts variables is also analyzed.
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.