The study of higher-order resonant and non-resonant boundary value problems

The existence of at least one solution to a nonlinear $n^\textrm{th}$ order differential equation $x^{(n)} = f(t,x,x',\ldots,x^{(n-1)}), \ 0 <t<1$, under both non-resonant and resonant boundary conditions, is proved. The methods involve the characterization of the $R_\delta$-set and an application of a new generalization for a multi-valued version of the Miranda Theorem

Measure pseudo affine-periodic solutions of semilinear differential equations

n this paper, we introduce the concept of pseudo affine-periodic functionvia measure theory, that is measure pseudo (Q, T)-affine-periodic function.Existence, uniqueness of measure pseudo (Q, T)-affine-periodic solutionfor semilinear differential equations are investigated.The working tools are based on the Banach contraction mapping principleand Leray-Schauder alternative theorem.Finally, an example is presented to illustrate the main findings

Modeling and forecasting riverine dissolved inorganic nitrogen export using anthropogenic nitrogen inputs, hydroclimate, and land-use change

A quantitative understanding of riverine nitrogen (N) export in response to human activities and climate change is critical for developing effective watershed N pollution control measures. This study quantified net anthropogenic N inputs (NANI) and riverine dissolved inorganic N (DIN=NO3-N+NH4-N+NO2-N) export for the upper Jiaojiang River catchment in eastern China over the 1980-2010 time period and examined how NANI, hydroclimate, and land-use practices influenced riverine DIN export. Over the 31-yr study period, riverine DIN yield increased by 1.6-fold, which mainly results from a ~77% increase in NANI and increasing fractional delivery of NANI due to a ~55% increase in developed land area. An empirical model that utilizes an exponential function of NANI and a power function of combining annual water discharge and developed land area percentage could account for 89% of the variation in annual riverine DIN yields in 1980-2010. Applying this model, annual NANI, catchment storage, and natural background sources were estimated to contribute 57%, 22%, and 21%, respectively, of annual riverine DIN exports on average. Forecasting based on a likely future climate change scenario predicted a 19.6% increase in riverine DIN yield by 2030 due to a 4% increase in annual discharge with no changes in NANI and land-use compared to the 2000-2010 baseline condition. Anthropogenic activities have increased both the N inputs available for export and the fractional export of N inputs, while climate change can further enhance riverine N export. An integrated N management strategy that considers the influence of anthropogenic N inputs, land-use and climate change is required to effectively control N inputs to coastal areas

Factors controlling phosphorus export from agricultural/forest and residential systems to rivers in eastern China, 1980–2011

This study quantified long-term response of riverine total phosphorus (TP) export to changes in land-use, climate, and net anthropogenic phosphorus inputs to agricultural/forest (NAPIAF) and residential (NAPIR) systems for the upper Jiaojiang watershed in eastern China. Annual NAPIAF rose by 73% in 1980-1999 followed by a 41% decline in 2000-2011, while NAPIR continuously increased by 122% over the 1980-2011 period. Land-use showed a 63% increase in developed land area (D%) and a 91% increase in use of efficient drainage systems on agricultural land area (AD%) over the study period. Although no significant trends were observed in annual river discharge or precipitation, the annual number of storm events rose by 90% along with a 34% increase in the coefficient of variation of daily rainfall. In response to changes of NAPIAF, NAPIR, land-use and precipitation patterns, riverine TP flux increased 16.0-fold over the 32-year record. Phosphorus export via erosion and leaching was the dominant pathway for P delivery to rivers. An empirical model incorporating annual NAPIAF, NAPIR, precipitation, D%, and AD% was developed (R2=0.96) for apportioning riverine TP sources and predicting annual riverine TP fluxes. The model estimated that NAPIAF, NAPIR and legacy P sources contributed 19-56%, 16-67% and 13-32% of annual riverine TP flux in 1980-2011, respectively. Compared to reduction of NAPIAF, reduction of NAPIR was predicted to have a greater immediate impact on decreasing riverine TP fluxes. Changes in anthropogenic P input sources (NAPIAF vs. NAPIR), land-use, and precipitation patterns as well as the legacy P source can amplify P export from landscapes to rivers and should be considered in developing P management strategies to reduce riverine P fluxes

Influence of Lag Effect, Soil Release, And Climate Change on Watershed Anthropogenic Nitrogen Inputs and Riverine Export Dynamics

This study demonstrates the importance of the nitrogen-leaching lag effect, soil nitrogen release, and climate change on anthropogenic N inputs (NANI) and riverine total nitrogen (TN) export dynamics using a 30-yr record for the Yongan River watershed in eastern China. Cross-correlation analysis indicated a 7-yr, 5-yr, and 4-yr lag time in riverine TN export in response to changes in NANI, temperature, and drained agricultural land area, respectively. Enhanced by warmer temperature and improved agricultural drainage, the upper 20 cm of agricultural soils released 270 kg N ha(-1) between 1980 and 2009. Climate change also increased the fractional export of NANI to river. An empirical model (R(2) = 0.96) for annual riverine TN flux incorporating these influencing factors estimated 35%, 41%, and 24% of riverine TN flux originated from the soil N pool, NANI, and background N sources, respectively. The model forecasted an increase of 45%, 25%, and 6% and a decrease of 13% in riverine TN flux from 2010 to 2030 under continued development, climate change, status-quo, and tackling scenarios, respectively. The lag effect, soil N release, and climate change delay riverine TN export reductions with respect to decreases in NANI and should be considered in developing and evaluating N management measures

Piecewise weighted pseudo almost periodic solutions of impulsive integro-differential equations via fractional operators

In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented

Measure pseudo affine-periodic solutions of semilinear differential equations

n this paper, we introduce the concept of pseudo affine-periodic functionvia measure theory, that is measure pseudo (Q, T)-affine-periodic function.Existence, uniqueness of measure pseudo (Q, T)-affine-periodic solutionfor semilinear differential equations are investigated.The working tools are based on the Banach contraction mapping principleand Leray-Schauder alternative theorem.Finally, an example is presented to illustrate the main findings