Search results for "maximum"
showing 10 items of 753 documents
Gemcitabine and cisplatin versus vinorelbine and cisplatin versus ifosfamide+gemcitabine followed by vinorelbine and cisplatin versus vinorelbine and…
2003
Abstract Purpose: we carried out a phase III randomized trial to compare vinorelbine–cisplatin regimen to gemcitabine–cisplatin regimen, and to a sequential administration of gemcitabine–ifosfamide followed by vinorelbine–cisplatin or the opposite sequence of vinorelbine–cisplatin followed by ifosfamide–gemcitabine according to the ‘worst drug rule’ hypothesis in patients with locally advanced unresectable stage IIIB or metastatic stage IV non-small cell lung cancer. The primary endpoint was survival parameters, while secondary endpoints included analysis of response rates and toxicity. Patients and methods: patients were randomized to receive: (a) gemcitabine 1000 mg/m2 on days 1, 8 and 15…
Principal eigenvalue of a very badly degenerate operator and applications
2007
Abstract In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator Δ ∞ u = ( D 2 u D u | D u | ) ⋅ D u | D u | . This operator arises from the optimal Lipschitz extension problem and it plays the same fundamental role in the calculus of variations of L ∞ functionals as the usual Laplacian does in the calculus of variations of L 2 functionals. Our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of Berestycki, Nirenberg and Varadhan [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operator…
Generalized Harnack inequality for semilinear elliptic equations
2015
Abstract This paper is concerned with semilinear equations in divergence form div ( A ( x ) D u ) = f ( u ) , where f : R → [ 0 , ∞ ) is nondecreasing. We introduce a sharp Harnack type inequality for nonnegative solutions which is a quantified version of the condition for strong maximum principle found by Vazquez and Pucci–Serrin in [30] , [24] and is closely related to the classical Keller–Osserman condition [15] , [22] for the existence of entire solutions.
Positive solutions for the Neumann p-Laplacian
2017
We examine parametric nonlinear Neumann problems driven by the p-Laplacian with asymptotically ( $$p-1$$ )-linear reaction term f(z, x) (as $$x\rightarrow +\infty $$ ). We determine the existence, nonexistence and minimality of positive solutions as the parameter $$\lambda >0$$ varies.
Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential
2020
AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.
Markov extensions for multi-dimensional dynamical systems
1999
By a result of F. Hofbauer [11], piecewise monotonic maps of the interval can be identified with topological Markov chains with respect to measures with large entropy. We generalize this to arbitrary piecewise invertible dynamical systems under the following assumption: the total entropy of the system should be greater than the topological entropy of the boundary of some reasonable partition separating almost all orbits. We get a sufficient condition for these maps to have a finite number of invariant and ergodic probability measures with maximal entropy. We illustrate our results by quoting an application to a class of multi-dimensional, non-linear, non-expansive smooth dynamical systems.
Solutions and positive solutions for superlinear Robin problems
2019
We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.
A multiplicity theorem for parametric superlinear (p,q)-equations
2020
We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.
Conflicting coccolithophore and geochemical evidence for productivity levels in the Eastern Mediterranean sapropel S1
2011
Abstract The cyclic development of anoxic conditions in the eastern Mediterranean deep sea waters is one of the most fascinating research topics in paleoceanographic studies. In combination with bottom water stagnation, enhanced primary production is a common explanation for the deposition of organic-rich layers (sapropels). This is supported by extensive evidence from both geochemical and micropaleontological studies. The correspondence of recent sapropel layers with peaks of the lower photic zone coccolithophore species Florisphaera profunda has been interpreted as a proxy for the development of a deep chlorophyll maximum (DCM), due to the pycnocline/nutricline shallowing into the lower p…
A local post-retrieval tool for satellite precipitation estimates
2012
As illustrated by several literature case studies spread around di erent geographic locations, satellite precipi- tation estimates, obtained by means of consolidated algorithms, often result being considerably biased. Moreover observed bias is related to geographic location since particular features such as latitude, presence of coastal areas and climatological and weather regime, a ect performances of satellite estimates. Bias adjusted products that make use of global ground-based precipitation estimates, are available as well but still these datasets may show a relevant bias level. In this study a procedure to bias-adjust satellite precipitation estimates has been devel- oped for the loca…