1,721,011 research outputs found
Traveling waves for highly degenerate and singular reaction-diffusion-advection equations with discontinuous coefficients
No full textSufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are furnished. Under an additional hypothesis on the convection term, the set of admissible wave speeds is characterized in terms of the minimum wave speed, which is estimated through a double-sided bound. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies
Remarks on growth conditions in calculus of variations
No full textWe discuss some classical growth assumptions for the integrands of the calculus of variations and compare them with a new local condition we are introducing in the present paper. Our existence result has great advantages with respect to applications, as examples show
Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem
Full text linkIn this paper we investigate the boundary eigenvalue problem x''-b(c,t,x)x'+g(t,x)=0, x(-∞)=0, x(+∞)=1 depending on the real parameter c. We take the function b continuous and positive and assume that g is bounded and becomes active and positive only when it exceeds a threshold value theta in (0,1). At the point theta we allow g to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when b=c+h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included.In this paper we investigate the boundary eigenvalue problem (equation presented) depending on the real parameter c. We take β continuous and positive and assume that g is bounded and becomes active and positive only when x exceeds a threshold value θ ∈]0,1[. At the point θ we allow g(t, · ) to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values c for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when β reduces to c + h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included
On mixed problem for first order partial differential functional equations
No full textWeakly coupled first-order partial functional-differential systems are considered. A mixed problem under Carathe'odory and Volterra assumptions is investigated. A comparison theorem in a generalized Haar pyramid is presented. Extremal solutions of some ordinary functional-differential systems play the role of comparison function. As an application, uniqueness and continuous dependence criteria for generalized solutions are derived
Boundary value problems for strongly nonlinear equations under a Wintner-Nagumo growth condition
Full text linkAbstract We study the following strongly nonlinear differential equation: ( a ( t , x ( t ) ) Φ ( x ′ ( t ) ) ) ′ = f ( t , x ( t ) , x ′ ( t ) ) , a.e. in [ 0 , T ] subjected to various boundary conditions including, as particular cases, the classical Dirichlet, periodic, Neumann and Sturm-Liouville problems. We adopt the method of lower and upper solutions requiring a weak form of a Wintner-Nagumo growth condition
Interaction among the theories of ordinary differential equations in various hereditary settings
No full textIn a previous paper (of the same authors) the equivalence of very different formulations for hereditary differential structures was proved. Here we discuss a deeper level of equivalence. In force of the present results the theories already developed for the various structures are essentially interchangeable, with remercable advantages from both theoretical and applied point of view
On the equivalence of different classes of hereditary systems
No full textWe summarize and illustrate the advantages of some previous results (by the same authors) on the equivalence of different classes of hereditary systems which appeared not comparable
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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