Equations to predict methane emissions from cows fed at maintenance energy level in pasture-based systems

Ruminant production is a vital part of food industry but it raises environmental concerns, partly due to the associated methane outputs. Efficient methane mitigation and estimation of emissions from ruminants requires accurate prediction tools. Equations recommended by international organizations or scientific studies have been developed with animals fed conserved forages and concentrates and may be used with caution for grazing cattle. The aim of the current study was to develop prediction equations with animals fed fresh grass in order to be more suitable to pasture-based systems and for animals at lower feeding levels. A study with 25 nonpregnant nonlactating cows fed solely fresh-cut grass at maintenance energy level was performed over two consecutive grazing seasons. Grass of broad feeding quality, due to contrasting harvest dates, maturity, fertilisation and grass varieties, from eight swards was offered. Cows were offered the experimental diets for at least 2 weeks before housed in calorimetric chambers over 3 consecutive days with feed intake measurements and total urine and faeces collections performed daily. Methane emissions were measured over the last 2 days. Prediction models were developed from 100 3-day averaged records. Internal validation of these equations, and those recommended in literature, was performed. The existing in greenhouse gas inventories models under-estimated methane emissions from animals fed fresh-cut grass at maintenance while the new models, using the same predictors, improved prediction accuracy. Error in methane outputs prediction was decreased when grass nutrient, metabolisable energy and digestible organic matter concentrations were added as predictors to equations already containing dry matter or energy intakes, possibly because they explain feed digestibility and the type of energy-supplying nutrients more efficiently. Predictions based on readily available farm-level data, such as liveweight and grass nutrient concentrations were also generated and performed satisfactorily. New models may be recommended for predictions of methane emissions from grazing cattle at maintenance or low feeding levels.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Averaging for retarded functional differential equations

We consider retarded functional differential equations in the setting of Kurzweil-Henstock integrable functions and we state an averaging result for these equations. Our result generalizes previous ones. (C) 2011 Elsevier Inc. All rights reserved.

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given. (c) 2007 Elsevier Ltd. All rights reserved.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

STABILITY FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class of equations with GODEs.

Schrodinger-Poisson equations without Ambrosetti-Rabinowitz condition

We prove the existence of ground state solutions for a stationary Schrodinger-Poisson equation in R(3). The proof is based on the mountain pass theorem and it does not require the Ambrosetti-Rabinowitz condition. (C) 2010 Elsevier Inc. All rights reserved.

Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.