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Level of resistance Look at Principal Kinds versus The southern area of Rice Black-Streaked Dwarf Malware throughout Southeast China.
In the paper, we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form Ax ∈ F(x), x ∈ U, where [Formula see text] is an m-accretive operator in a Banach space E, [Formula see text] is a weakly upper semicontinuous set-valued map constrained to an open subset U of a closed set K ⊂ E. Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.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'.In this paper, we investigate the dynamical properties associated with planar maps which can be represented as a composition of twist maps together with expansive-contractive homeomorphisms. The class of maps we consider present some common features both with those arising in the context of the Poincaré-Birkhoff theorem and those studied in the theory of topological horseshoes. In our main theorems, we show that the multiplicity results of fixed points and periodic points typical of the Poincaré-Birkhoff theorem can be recovered and improved in our setting. In particular, we can avoid assuming area-preserving conditions and we also obtain higher multiplicity results in the case of multiple twists. Applications are given to periodic solutions for planar systems of non-autonomous ODEs with sign-indefinite weights, including the non-Hamiltonian case. The presence of complex dynamics is also discussed. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.We prove the existence of multiple positive solutions of nonlinear second-order nonlocal boundary value problems with nonlinear term having derivative dependence. We allow the nonlinearity to grow quadratically with respect to derivatives. find more We obtain a priori bounds for norms of derivatives by using a recently obtained Gronwall-type inequality. Three examples illustrate some of the results. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg-Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.We extend to delay equations recent results obtained by G. Feltrin and F. Zanolin for second-order ordinary equations with a superlinear term. We prove the existence of positive periodic solutions for nonlinear delay equations -u″(t) = a(t)g(u(t), u(t - τ)). We assume superlinear growth for g and sign alternance for a. The approach is topological and based on Mawhin's coincidence degree. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.Venous ulcers in lower legs remain a profound treatment problem in contemporary medicine. Proper healing requires, among other things, sufficient blood supply and provision of suitable amount of oxygen to the treated tissues. The aim of the study was to assess the influence of combined physical therapy applied in patients with chronic venous leg ulcers on the oxygen partial pressure values. Fifty-four patients (25 females and 29 males), in the age range of 38 to 89 years with chronic venous leg ulcers, underwent a cycle of 15 procedures with the use of Laserobaria-S device. During a procedure, the patient's lower limb was simultaneously exposed to oxygen having the pressure of 1.5 ATA, low-frequency magnetic field, and low-energy light radiation. Before procedures, directly after the first procedure, as well as on completion of the entire therapeutic cycle, the patients underwent oxygen partial pressure measurements in the tissues surrounding the ulceration area, by means of transcutaneous oximetry, with the use of Medicap Précise 8008s device. The combined physical therapy shows a statistically significant increase of oxygen partial pressure values in tissues surrounding the ulceration, from the average of 68.63 ± 17.04 mm Hg before commencing the therapeutic cycle, to the average of 74.20 ± 18.92 mm Hg after the first procedure (P less then .001) and to the average value of 83.79 ± 20.74 mm Hg (P less then .001) after completion of therapeutic cycle. Combined physical therapy procedures cause a statistically significant increase of oxygen partial pressure values in tissues surrounding the ulceration, assessed using the objective method of transcutaneous oximetry, both in women and men.
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