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Globally positive unbounded solutions, with zero derivative at infinity, are here considered for ordinary differential equations involving the generalized Euclidean mean curvature operator. When p ≥ 2 , the results highlight an analogy with an auxiliary equation with the p-Laplacian operator. The results are obtained using some comparison criteria for the principal solutions of a class of associated half-linear equations. [ABSTRACT FROM AUTHOR]

Ultrawideband radar is commonly used in the frequency range of 50-500 MHz to detect buried pipes at a depth of about 1-2 m depending on the soil characteristics. The typical feature used to locate the pipes is the hyperbolic pattern of the time of flight generated by a linear scan of the antenna above the surface. When the pipes are close together, the hyperbolas overlap, anda straightforward least squares fit is not possible. The Hough transform provides one possible solution. This paper extends the Hough transform by introducing a weighting factor depending on the differentials of the unknown parameters with respect to the experimental errors, namely, the probe position error and the time-of-flight error. This enables optimally placed sets of data pairs to be given greater weight than 'ill-conditioned' sets, as for example when all data pairs lie near one end of the arc. The result is a decrease in the background amplitude with respect to the maximum of the peaks in the Hough accumulator space. It is shown that this improvement persists even when many arcs are present. A mathematical analysis with analytical results is given for the case of four unknowns: pipe radius R, pipe center position (Y, Z), and soil propagation velocity V. The results are presented through simulations introducing controlled uncertainties in the probe position, the time of flight, and its bin size. The simulations demonstrate the correlations that occur between the radius, depth, and velocity for given experimental uncertainties. Index Terms--Algorithms, buried objects, equations, ground-penetrating radar (GPR), Hough transforms, radar data processing, radar measurements.

Necessary and sufficient conditions for regular or slow variation of all positive solutions of a second-order linear difference equation with arbitrary sign coefficient are established. Relations with the so-called -classification are also analyzed and a generalization of the results to the half-linear case completes the paper.

A general method for solving boundary value problems associated to functional difference systems on the discrete half-line is presented and applied in studying the existence of positive unbounded solutions for a system of two coupled nonlinear difference equations. A further example, illustrating the method, completes the paper.

The paper deals with the nonlinear differential equation (a(t) Φ (x'))' + b(t)F (x) = 0, t ∈ [1, ∞), in the case when the weight b has indefinite sign. In particular, the problem of the existence of the so-called globally positive Kneser solutions, that is solutions x such that x(t) > 0, x1(t) < 0 on the whole closed interval [1, ∞), is considered. Moreover, conditions assuring that these solutions tend to zero as t → ∞ are investigated by a Schauder's half-linearization device jointly with some properties of the principal solution of an associated half-linear differential equation. The results cover also the case in which the weight b is a periodic function or it is unbounded from below. [ABSTRACT FROM AUTHOR]

Under the assumption that the coefficients are regularly varying functions, existence and asymptotic form of strongly decreasing solutions are here studied for a system of two coupled nonlinear second-order equations of Emden-Fowler type, satisfying a subhomogeneity condition. Several examples of application of the main result and a comparison with existing literature complete the paper. [ABSTRACT FROM AUTHOR]

The problem of oscillation of a second order nonlinear difference system is considered and conditions for oscillation are derived by means of a complete analysis of nonoscillatory solutions. The case of systems with deviating arguments is also analyzed, and the results are shown to significantly generalize some existing ones. [Copyright &y& Elsevier]

A boundary value problem associated with the difference equation with advanced argument [Formula: see text] is presented, where Φ ( u ) = | u | α sgn u , α  > 0, p is a positive integer and the sequences a , b , are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.