Positive solutions for a multi-point eigenvalue problem involving the one dimensional pp-Laplacian

A multi-point boundary value problem involving the one dimensional $p$-Laplacian and depending on a parameter is studied in this paper and existence of positive solutions is established by means of a fixed point theorem for operators defined on Banach spaces with cones

Lyapunov-type inequalities for quasilinear systems with antiperiodic boundary conditions

We establish some new Lyapunov-type inequalities for one-dimensional p-Laplacian systems with antiperiodic boundary conditions. The lower bounds of eigenvalues are presented.Встановлено дєякі нові нєрівності типу Ляпунова для одновимірних p-лапласових систем з антиперіодичними граничними умовами. Наведено нижні межі для власних значень

Multiple positive solutions for a nonlinear 2n-th order m-point boundary value problems

In this paper, we consider the existence of multiple positive solutions for the 2n-th order $m$-point boundary value problems: $$\left\{\begin{array}{ll} x^{(2n)}(t)=f(t,x(t),x^{''}(t),\cdots ,x^{(2(n-1))}(t)), 0\leq t\leq 1,\\ x^{(2i+1)}(0)=\sum\limits_{j=1}^{m-2}\alpha_{ij}x^{(2i+1)}(\xi_j),\quad x^{(2i)}(1)=\sum\limits_{j=1}^{m-2}\beta_{ij}x^{(2i)}(\xi_j), 0\leq i\leq n-1,\\ \end{array}\right.$$ where $\alpha_{ij}, \beta_{ij} \ (0\leq i\leq n-1,1\leq j\leq m-2) \in [0,\infty)$, $\sum\limits_{j=1}^{m-2}\alpha_{ij},\sum\limits_{j=1}^{m-2}\beta_{ij}\in (0,1)$, $0<\xi_1<\xi_2<\ldots<\xi_{m-2}<1$. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem

Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian

AbstractWe consider the boundary value problems: (ϕp(x′(t)))′+q(t)f(t,x(t),x(t−1),x′(t))=0, ϕp(s)=|s|p−2s, p>1, t∈(0,1), subject to some boundary conditions. By using a generalization of the Leggett–Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above problems

Lyapunov-type inequalities for (m+1)(m+1)th order half-linear differential equations with anti-periodic boundary conditions

In this work, we will establish several new Lyapunov-type inequalities for $(m+1)$th order half-linear differential equations with anti-periodic boundary conditions, the results of this paper are new and generalize and improve some early results in the literature

Seasonal variation of the deep limb of the Pacific Meridional Overturning circulation at Yap-Mariana junction

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Wang, J., Ma, Q., Wang, F., Lu, Y., & Pratt, L. J. Seasonal variation of the deep limb of the Pacific Meridional Overturning circulation at Yap-Mariana junction. Journal of Geophysical Research: Oceans, 125(7), (2020): e2019JC016017, doi:10.1029/2019JC016017.This study reveals the seasonal variability of the lower and upper deep branches of the Pacific Meridional Overturning Circulation (L‐PMOC and U‐PMOC) in the Yap‐Mariana Junction (YMJ) channel, a major gateway for deep flow into the western Pacific. On the western side of the YMJ channel, mooring observations in 2017 and in 1997 show the seasonal phase of the L‐PMOC at depths of 3,800–4,400 m: strong northward flow with speed exceeding 20 cm s−1 and lasting from December to next May and weak flow during the following 6 months. On the eastern side of the channel, mooring observations during 2014–2017 show two southward deep flows with broadly seasonal phases, one being the return flow of L‐PMOC below ~4,000 m and with the same phase of L‐PMOC but reduced magnitude. The second, shallower, southward deep flow corresponds to the U‐PMOC observed within 3,000–3,800 m and with opposite phase of L‐PMOC, that is, strong (weak) southward flow appearing during June–November (December–May). Seasonal variations of the L‐PMOC and U‐PMOC are accompanied by the seasonal intrusions of the Lower and Upper Circumpolar Waters (LCPW and UCPW) in lower and upper deep layers, which change the isopycnal structure and the deep currents in a way consistent with geostrophic balance.This study is supported by the National Natural Science Foundation of China (grants 91958204 and 41776022), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant XDA22000000), the Key Research Program of Frontier Sciences, CAS (grant QYZDB‐SSW‐SYS034). F. Wang thanks the support from the Scientific and Technological Innovation Project by Qingdao National Laboratory for Marine Science and Technology (grant 2016ASKJ12), the National Program on Global Change and Air‐Sea Interaction (grant GASI‐IPOVAI‐01‐01), and the National Natural Science Foundation of China (grants 41730534 and 41421005). L. Pratt gratefully acknowledges the support by NSF (grant OCE‐1657870). Jianing Wang and Qiang Ma contributed equally to this work

Pathways, volume transport, and seasonal variability of the lower deep limb of the Pacific Meridional Overturning Circulation at the Yap-Mariana Junction

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Wang, J., Wang, F., Lu, Y., Ma, Q., Pratt, L. J., & Zhang, Z. Pathways, volume transport, and seasonal variability of the lower deep limb of the Pacific Meridional Overturning Circulation at the Yap-Mariana Junction. Frontiers in Marine Science, 8, (2021): 672199, https://doi.org/10.3389/fmars.2021.672199.The lower deep branch of the Pacific Meridional Overturning Circulation (L-PMOC) is responsible for the deep-water transport from Antarctic to the North Pacific and is a key ingredient in the regulation of global climate through its influence on the storage and residence time of heat and carbon. At the Pacific Yap-Mariana Junction (YMJ), a major gateway for deep-water flowing into the Western Pacific Ocean, we deployed five moorings from 2018 to 2019 in the Eastern, Southern, and Northern Channels in order to explore the pathways and variability of L-PMOC. We have identified three main patterns for L-PMOC pathways. In Pattern 1, the L-PMOC intrudes into the YMJ from the East Mariana Basin (EMB) through the Eastern Channel and then flows northward into the West Mariana Basin (WMB) through the Northern Channel and southward into the West Caroline Basin (WCB) through the Southern Channel. In Pattern 2, the L-PMOC intrudes into the YMJ from both the WCB and the EMB and then flows into the WMB. In Pattern 3, the L-PMOC comes from the WCB and then flows into the EMB and WMB. The volume transports of L-PMOC through the Eastern, Southern, and Northern Channels all exhibit seasonality. During November–April (May–October), the flow pathway conforms to Pattern 1 (Patterns 2 and 3), and the mean and standard deviation of L-PMOC transports are −4.44 ± 1.26 (−0.30 ± 1.47), −0.96 ± 1.13 (1.75 ± 1.49), and 1.49 ± 1.31 (1.07 ± 1.10) Sv in the Eastern, Southern, and Northern Channels, respectively. Further analysis of numerical ocean modeling results demonstrates that L-PMOC transport at the YMJ is forced by a deep pressure gradient between two adjacent basins, which is mainly determined by the sea surface height (SSH) and water masses in the upper 2,000-m layer. The seasonal variability of L-PMOC transport is attributed to local Ekman pumping and westward-propagating Rossby waves. The L-PMOC transport greater than 3,500 m is closely linked to the wind forcing and the upper ocean processes.This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (grant XDA22000000), the National Natural Science Foundation of China (grants 91958204 and 41776022), the Key Research Program of Frontier Sciences, CAS (grant QYZDB-SSW-SYS034), and the International Partnership Program of CAS (grant 133137KYSB20180056). FW thanks the support from the National Natural Science Foundation of China (grants 41730534 and 41421005). QM thanks the support by the National Natural Science Foundation of China (grant 42006003)