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We study global bifurcation from intervals for the following fully nonlinear elliptic problem with Pucci's operator {-Mλ,Λ+(D²u)=μu+h(u,μ)+g(u,μ)u=0inΩ,on∂Ω, where h is not necessarily differentiable at the origin or infinity with respect to u. Furthermore, under some suitable assumptions on nonlinearity, we investigate the global structure of bifurcating branches, which can be used to obtain the existence of one-sign solution. [ABSTRACT FROM AUTHOR]

In this article, we consider a Dancer-type unilateral global bifurcation for the Kirchhoff-type problem .... Under natural hypotheses on h, we show that (aλk, 0) is a bifurcation point of the above problem. As applications we determine the interval of λ, in which there exist nodal solutions for the Kirchhoff-type problem ..., where f is asymptotically linear at zero and is asymptotically 3-linear at infinity. To do this, we also establish a complete characterization of the spectrum of a nonlocal eigenvalue problem. [ABSTRACT FROM AUTHOR]

We study the unilateral global bifurcation for the nonlinear Sturm- Liouville problem -(pu')' + qu = λau + af(x, u, u', λ) + g(x, u, u', λ) x ∈ (0, 1), b0u(0) + c0u'(0) = 0, b1u(1) + c1u'(1) = 0, where a ∈ C[0,1], [0,+∞)) and (x) ... 0 on any subinterval of [0, 1], f, g ∈ C[0, 1] x ℝ³, ℝ) and f is not necessarily differentiable at the origin or infinity with respect to u. Some applications are given to nonlinear second-order two- point boundary-value problems. This article is a continuation of. [ABSTRACT FROM AUTHOR]

In this paper, we study unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity for nonlinear Sturm-Liouville problems of the form {-(pu')' + qu = λ au + af (x, u, u', λ) + g (x, u, u', λ) for x ∈ (0, 1), b0 (0) + c0u' (0) = 0, b1u(1) + c1u '(1) = 0, where a ∈C([0, 1], [0,+∞)) and a(x) ... 0 on any subinterval of [0, 1], f, g ∈C([0, 1] ℝ³ ℝ ). Suppose that f and g satisfy |f(x, ξηλ)≤ M0 |ξ?| +M1 |η|, ... x ∈ [0, 1] and λ∈ℝ, as either |ξ| + |η→ 0 or |ξ| + |η→ + ∞, for some constants M 0, M1, and any bounded interval Λ. [ABSTRACT FROM AUTHOR]

In this article, we study elliptic problems with discontinuous non-linearities involving the p-Laplacian both in bounded and unbounded domains. We prove that there exists a global branch of positive solutions under some suitable assumptions of the nonlinearities. Our results extend the corresponding ones of the Laplacian due to Ambrosetti, et al. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlocal semilinear elliptic problems with in-homogeneous strong Allee effect. By means of variational approach, we prove that the problem has at least two positive solutions for large λ under suitable hypotheses about nonlinearity. We also prove some nonexistence results. In particular, we give a positive answer to the conjecture of Liu-Wang-Shi. [ABSTRACT FROM AUTHOR]

We prove existence and multiplicity of positive solutions for semipositone problems involving p-Laplacian in a bounded smooth domain of ℝN under the cases of sublinear and superlinear nonlinearities term. [ABSTRACT FROM AUTHOR]

In this article we consider the differential inclusion -div(|∇u|p(x)-2∇u) ∈ ∂F(x, u) in Ω, u = 0 on ∂Ω which involves the p(x)-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in W01,p(x) (Ω). [ABSTRACT FROM AUTHOR]

Characterizing the key determinants of variability in the exposure of orally administered drugs may be important in understanding the implications of exposure variability on clinical responses. In particular, partitioning overall variability into interoccasion variability (IOV) and interindividual variability (IIV) allows a better assessment of the clinical importance of exposure variability. The IOV characterizes the dose-to-dose variability in exposure within a subject and is likely to be less clinically relevant than IIV for chronically administered drugs as the effect of IOV averages out over repeated dosing. The main aims of this model-based analysis were (1) to characterize the IOV and IIV of dasatinib, a novel, orally administered, multitargeted kinase inhibitor of BCR-ABL and SRC family kinases that is indicated for the treatment of chronic myeloid leukemia and Philadelphia-positive acute lymphoblastic leukemia and (2) to demonstrate using simulated data that it is possible to estimate IIV and IOV in relative bioavailability (FR) of an orally administered drug, given an adequate sampling scheme. Variability in dasatinib exposure was estimated to be mainly due to IOV in FR (44% coefficient of variation [CV]) and, to a lesser extent, due to IIV in FR and IIV in clearance (32% and 25% CV, respectively). The IIV is expected to be more clinically relevant than IOV for chronically administered oral drugs such as dasatinib, as the overall variability in cumulative exposure will be mainly due to IIV. The analysis of simulated data demonstrated that models ignoring either IIV or IOV in FR resulted in upwardly biased estimates of interindividual or residual variability. Thus, it may be important to account for both IIV and IOV in FR, particularly for orally administered agents that exhibit absorption-related variability in exposure. [ABSTRACT FROM AUTHOR]

We establish a unilateral global bifurcation result for the following problem where Ω is a bounded domain in . Based on this global bifurcation result, we also studied the global structure of one-sign solutions according to different asymptotic behaviors (sublinear/linear/superlinear/jumping) nonlinearity near zero. [ABSTRACT FROM AUTHOR]

In this paper, we shall study unilateral global bifurcation phenomenon for the following homogeneous Kirchhoff type problem (− ∫R 1 0∣u'∣2dx)u'' = λu3 + h(x, u, λ) in (0, 1),u(0) = u(1) = 0.As application of bifurcation result, we shall determine the interval of λ in which there exist nodal solutions for the following homogeneous Kirchhoff type problem (−∫R 10∣u'∣2dx)u'' = λ f(x, u) in (0, 1),u(0) = u(1) = 0,where f is asymptotically cubic at zero and infinity. To do this, we also establish a complete characterization of the spectrum of a homogeneous nonlocal eigenvalue problem. [ABSTRACT FROM AUTHOR]

We consider the systems of (-1)mu(2m) = λu + λv + uf(t,u,v), t ∈ (0,1), u(2i)(0) = u(2i)(1) = 0, and 0 ≤ i ≤ m-1, (-1)mv(2m) = μu + μv + vg(t,u,v), t ∈ (0,1), v(2i)(0) = v(2i)(1) = 0, 0 &38804; i ≤ m-1, where λ,μ ∈ R are real parameters. f, g : [0,1] x R2 → R are Ck,k ≥ 3 functions and f(t,0,0) = g (t,0,0) = 0, t ∈ [0,1]. It will be shown that if the functions, f and g are "generic" then the solution set of the systems consists of a countable collection of 2-dimensional, Ck manifolds. [ABSTRACT FROM AUTHOR]

Background: SHetA2 {[(4-nitrophenyl)amino][2,2,4,4-tetramethylthiochroman-6-yl)amino]methane-thione], NSC 726189} is a sulfur-containing heteroarotinoid, which selectively inhibits cancer cell growth and induces apoptosis without activation of nuclear retinoic acid receptors (RARs). The objective was to develop and validate a HPLC/UV method for the determination of SHetA2, and study the pharmacokinetics of SHetA2 in the mouse. Methods: SHetA2 and the internal standard, methylated XK469 (MeXK469) were isolated from 0.2 ml of mouse plasma by solid phase extraction. The analytes were separated on a narrow-bore C18 column, with the mobile phase consisting of 60% acetonitrile in water at a flow rate of 0.2 ml/min. UV detection was set at 341 nm. Pharmacokinetic studies of SHetA2 were carried out in mice following i.v. bolus dose at 20 mg/kg and oral administrations at 20 and 60 mg/kg. Results: The standard curves were linear between 25 and 2,500 nM and the lower limit of quantification (LLOQ) was 25 nM. The within-run coefficients of variation (CVs) were 11.1% at 10, 9.4% at 100, and 5.2% at 2,500 nM and the respective between-run CVs were 10.9, 3.1, and 1.5% (all n=5). The recovery was 85.8% for SHetA2 and 80.6% for MeXK469. Following i.v. bolus dose, plasma concentrations of ~10 μM were achieved at 5 min in mice and declined biexponentially with detectable levels at 60 h. The data were fitted with a two-compartment model, which gave a mean initial t 1/2 of 40 min and terminal t 1/2 of 11.4 h ( n=6). The total body clearance was ~1.81 l/h/kg. The volume of distribution at steady state ( V dss) was 20.8 l/kg. Plasma protein binding was found to be 99.3–99.5% at low micromolar concentrations. Plasma concentration data for the i.v. and p.o. doses were also fitted interactively to a two-compartment deconvolution model. From this result, oral bioavailability values of 15% at 20 mg/kg and 19% at 60 mg/kg were obtained. Conclusions: A highly sensitive HPLC/UV method for the quantification of SHetA2 in plasma has been developed to support pharmacokinetics of SHetA2 in the mouse. Pharmacokinetic behaviors of this drug appear to be favorable for future development. [ABSTRACT FROM AUTHOR]