Existence of positive, negative and sign-changing periodic solutions for a class of integral equations

AbstractIn this paper, the simultaneous existence of positive, negative and sign-changing periodic solutions for a class of integral equations of the form ϕ(x)=∫[x,x+ω]∩ΩK(x,y)f(y,ϕ(y−τ(y)))dy,x∈Ω, is considered, where Ω is a closed subset of RN with a periodic structure. Our main result is different from most existing results since they provide three constant sign periodic solutions only

Periodic Solutions for a System of Difference Equations

This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory

Existence and Uniqueness of Periodic Solutions of Mixed Monotone Functional Differential Equations

This paper deals with the existence and uniqueness of periodic solutions for the first-order functional differential equation ()=−()()+1(,(−()))+2(,(−())) with periodic coefficients and delays. We choose the mixed monotone operator theory to approach our problem because such methods, besides providing the usual existence results, may also sometimes provide uniqueness as well as additional numerical schemes for the computation of solutions

Snow Accumulation Rate on Qomolangma (Mount Everest), Himalaya: Synchroneity With Sites Across the Tibetan Plateau on 50-100 Year Timescales

Annual-layer thickness data, spanning AD 1534-2001, from an ice core from East Rongbuk Coll on Qomolangma (Mount Everest, Himalaya) yield an age-depth profile that deviates systematically from a constant accumulation-rate analytical model. The profile clearly shows that the mean accumulation rate has changed every 50-100 years. A numerical model was developed to determine the magnitude of these multi-decadal-scale rates. The model was used to obtain a time series of annual accumulation. The mean annual accumulation rate decreased from similar to 0.8 m ice equivalent in the 1500s to similar to 0.3 m in the mid-1800s. From similar to 1880 to similar to 1970 the rate increased. However, it has decreased since similar to 1970. Comparison with six other records from the Himalaya and the Tibetan Plateau shows that the changes in accumulation in East Rongbuk Col are broadly consistent with a regional pattern over much of the Plateau. This suggests that there may be an overarching mechanism controlling precipitation and mass balance over this area. However, a record from Dasuopu, only 125 km northwest of Qomolangma and 700 m higher than East Rongbuk Col, shows a maximum in accumulation during the 1800s, a time during which the East Rongbuk Col and Tibetan Plateau ice-core and tree-ring records show a minimum. This asynchroneity may be due to altitudinal or seasonal differences in monsoon versus westerly moisture sources or complex mountain meteorology

Recent Increases in Atmospheric Concentrations of Bi, U, Cs, S and Ca from a 350-Year Mount Everest Ice Core Record

High-resolution major and trace elements (Sr, Cs, Ba, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu, Bi, U, Tl, Al, S, Ca, Ti, V, Cr, Mn, Fe, and Co) quantified in a Mount Everest ice core ( 6518 m above sea level) spanning the period 1650-2002 AD provides the first Asian record of trace element concentrations from the pre-industrial era, and the first continuous high-resolution Asian record from which natural baseline concentrations and subsequent changes due to anthropogenic activities can be examined. Modern concentrations of most elements remain within the pre-industrial range; however, Bi, U, and Cs concentrations and their enrichment factors (EF) have increased since the similar to 1950s, and S and Ca concentrations and their EFs have increased since the late 1980s. A comparison of the Bi, U, Cs, S, and Ca data with other ice core records and production data indicates that the increase in atmospheric concentrations of trace elements is widespread, but that enrichment varies regionally. Likely sources for the recent enrichment of these elements include mining, metal smelting, oil and coal combustion, and end uses for Bi, and mining and refinement for U and Cs. The source of the synchronous enrichment of Ca and S is less certain, but may be related to land use and environmental change

Evidence for Recent Climate Change from Ice Cores in the Central Himalaya

Comparison of the terminus locations of Rongbuk Glacier, Mount Everest, measured in 1966 and 1997 shows that in the past 30 years the glacier has retreated 170-270 m, equivalent to a retreat speed of 5.5-8.7 m a−1. During summer 1997, a 15 m firn core was recovered from Dasuopu glacier (28°23′N, 85°44′E; 7000 m a.s.l.) on the northwest margin of Xixabangma Feng, Xizang (Tibet). The seasonal variations of δ18O values in the core indicate that monsoon signals are clearly recorded in the glacier. δ18O values are controlled by the amount effect in the monsoon season; more negative δ18O is representative of the monsoon season in snow layers. Analysis of the relationship between ice-core δ18O, sampled from 6500 m a.s.l. on the north side of Mount Everest, and instrumental series representing regional-scale precipitation, atmospheric circulation and temperature suggests a change in the relative influence of these parameters on δ18O since the 1940s. The results of the comparison add to and lengthen the sparse array of instrument data available for the Tibetan (Qinghai-Xizang) Plateau and demonstrate a recent decline in moisture flux for at least the southern part of the plateau. Glacier retreat, associated with a recent increase in temperature in the region, is coincident with this period of decreased moisture flux

Reduction in Northward Incursions of the South Asian Monsoon Since ~1400 AD Inferred from a Mt. Everest Ice Core

A highly resolved Mt. Everest ice core reveals a decrease in marine and increase in continental air masses related to relatively high summer surface pressure over Mongolia, and reduction in northward incursions of the summer South Asian monsoon since similar to 1400 AD. Previously published proxy records from lower sites south of the Himalayas indicate strengthening of the monsoon since this time. These regional differences are consistent with a south north seesaw in convective activity in the Asian monsoon region, and reflect a southward shift in the mean summer position of the monsoon trough since similar to 1400 AD. The change in monsoonal circulation at 1400 AD is synchronous with a reduction in solar irradiance and the onset of the LIA. This demonstrates a hemispheric scale circulation reorganization at this time, and the potential for future large shifts in monsoonal circulation

λ-Interval of Triple Positive Solutions for the Perturbed Gelfand Problem

We study a two-point Boundary Value Problem depending on two parameters that represents a mathematical model arising from the combustion theory. Applying fixed point theorems for concave operators, we prove uniqueness, existence, upper, and lower bounds of positive solutions. In addition, we give an estimation for the value of λ* such that, for the parameter λ∈[λ*,λ*], there exist exactly three positive solutions. Numerical examples are presented to illustrate various cases. The results complement previous work on this problem

Several Existence Theorems of Multiple Positive Solutions of Nonlinear <inline-formula> <graphic file="1687-2770-2009-584145-i1.gif"/></inline-formula>-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales

<p>Abstract</p> <p>By using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear <inline-formula> <graphic file="1687-2770-2009-584145-i2.gif"/></inline-formula>-point boundary value problem for the following second-order boundary value problem on time scales <inline-formula> <graphic file="1687-2770-2009-584145-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2009-584145-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2009-584145-i5.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2009-584145-i6.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2009-584145-i7.gif"/></inline-formula> is an increasing homeomorphism and homomorphism and <inline-formula> <graphic file="1687-2770-2009-584145-i8.gif"/></inline-formula>. Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems, respectively. In particular, our criteria generalize and improve some known results by Ma and Castaneda (2001). We must point out for readers that there is only the <inline-formula> <graphic file="1687-2770-2009-584145-i9.gif"/></inline-formula>-Laplacian case for increasing homeomorphism and homomorphism. As an application, one example to demonstrate our results is given.</p