1,720,980 research outputs found
Existence results for boundary value problems associated with singular strongly nonlinear equations
Full text linkWe consider a strongly nonlinear differential equation of the following general type: (Φ(a(t,x(t))x′(t)))′=f(t,x(t),x′(t)),a.e. on[0,T],where f is a Carathédory function, Φ is a strictly increasing homeomorphism (the Φ -Laplacian operator), and the function a is continuous and non-negative. We assume that a(t, x) is bounded from below by a non-negative function h(t), independent of x and such that 1 / h∈ Lp(0 , T) for some p> 1 , and we require a weak growth condition of Wintner–Nagumo type. Under these assumptions, we prove existence results for the Dirichlet problem associated with the above equation, as well as for different boundary conditions. Our approach combines fixed point techniques and the upper/lower solution method
An overview on spectral theory for nonlinear operators
No full text"We compare different spectral theories for nonlinear operators, focusing in particular on the notion of spectrum at a point recently introduced by the authors. We discuss the main properties of the nonlinear spectrum and present illustrating applications and examples.'
Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs
Full text linkWe discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results
A new spectrum for nonlinear operators in Banach spaces
No full textGiven any continuous self-map f of a Banach space E over K (where K is R or C)
and given any point p of E, we define a subset (f, p) of K, called the ‘spectrum of f at p’, which
coincides with the usual spectrum (f) of f in the linear case. More generally, we show that
(f, p) is always closed and, when f is C1, coincides with the spectrum (f0(p)) of the Fr´echet
derivative of f at p. Some applications to bifurcation theory are given and some peculiar examples
of spectra are provided
An affine Birkhoff--Kellogg type result in cones with applications to functional differential equations
Full text linkIn this short note we prove, by means of classical fixed point index, an
affine version of a Birkhoff--Kellogg type theorem in cones. We apply our
result to discuss the solvability of a class of boundary value problems for
functional differential equations subject to functional boundary conditions. We
illustrate our theoretical results in an example.Comment: 11 page
Global persistence of the unit eigenvectors of perturbed eigenvalue problems in hilbert spaces: The odd multiplicity case
No full textWe study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds
THE BROUWER DEGREE ASSOCIATED TO CLASSICAL EIGENVALUE PROBLEMS AND APPLICATIONS TO NONLINEAR SPECTRAL THEORY
No full textThanks to a connection between two completely different topics, the classical eigenvalue problem in a finite dimensional real vector space and the Brouwer degree for maps between oriented differentiable real manifolds, we are able to solve, at least in the finite dimensional context, a conjecture regarding global continuation in nonlinear spectral theory that we formulated in some recent papers. The infinite dimensional case seems nontrivial, and is still unsolved
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
Short-term effects of organic amendments on soil properties and maize (Zea maize L.) growth
Full text linkIn recent years, the application of biochar as soil amendment has generated a huge interest for the preservation of soil fertility by improving the physicochemical and biological properties of soil, and for the reduction of the negative effects of greenhouse emissions (climate-change adaptation). In this study, we investigated the effect of three soil amendments, namely, biochars derived from wood (BC), solid digestate (SD), and biochar derived from solid digestate (BSD), on soil parameters and their influence in maize-growth performance. The experiment was conducted in a greenhouse where organic amendments were applied to the soil control (C) at different application rates: 0%, 1%, 2%, and 3% w/w (equivalent at 0, 10, 20, and 30 t ha−1, respectively). The results indicated that all applications of organic amendments significantly enhanced soil parameters such as pH and electrical conductivity, while only BSD and SD showed a significant increase in secondary macro-(i.e., Ca, Mg) and micronutrient-element content (i.e., Na, Fe, Mn and Zn). The best maize performance (i.e., plant height, stem diameter, biomass dry weight, seed number, and weight per ear) was observed while using BSD, while plant growth in BC had reduced results, probably due to the low presence of elemental content and the relatively high volatile-matter (VM) content, which may have altered nitrogen dynamics
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