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This paper introduces a new concept of dual periodic boundary conditions. One of these conditions relates to the endpoints of an interval, while the other one involves two nonlocal positions within the interval. Under these boundary conditions, we establish the criteria for the existence of solutions for a fractional differential equation with p-Laplacian operator by using Mawhin's continuation theorem. An example is constructed for illustrating the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and uniqueness of solutions for several two-point fractional BVPs, including hybrid fractional BVP, sequential fractional BVP and so on. Using the Banach contraction mapping theorem, some sharp conditions that depend on the length of the given interval are presented, which ensure the uniqueness of solutions for the considered BVPs. Illustrative examples are also constructed. The results obtained in this study are noteworthy extensions of earlier works. [ABSTRACT FROM AUTHOR]

The large-scale uniform triangular prism-like CeO2 nanostructures with rough surface have been purposefully fabricated by a simple and efficient hydrothermal route. X-ray diffractometer (XRD), scanning electron microscope (SEM), X-ray photoelectron spectrum, Raman spectra and photoluminescence (PL) spectra were employed to research the obtained CeO2 samples. It is found that many Ce3+ ions and oxygen vacancies in the surface of cubic fluorite structure CeO2 samples. The possible mechanism involved the dissolution of rod-like structures and followed by the recrystallization of triangular prism-like structures was discovered. Ce3+ ions and oxygen vacancies may account for the similar broad photoluminescence emission bands for all samples, while their different emission intensity is attributed to the effects of morphology and size of the samples. [ABSTRACT FROM AUTHOR]

SO4 2−/TiO2–MxOy (M = Zr, Ce, La) were prepared by the precipitation-impregnation method and characterized by X-ray powder diffraction (XRD), Fourier transform infrared (FT-IR), and temperature-programmed desorption (NH3-TPD). Catalytic activities were evaluated in the acetalization of 1,3-propanediol (1,3-PD) with acetaldehyde and hydrolysis of 2-methyl-1,3-dioxane (2MD). SO4 2−/TiO2–ZrO2 (STZ) exhibited the best catalytic activity both in the acetalization and hydrolysis. With the molar ratio of Zr4+/Ti4+ = 1:4, the highest yields were 96.45% in 3 h and 93.68% of 2MD hydrolyzed in 18 h, in contrast to the yields lower than 60% by using other superacids. These results are consistent with the strongest acidity of the superacid containing Zr4+ among prepared superacids containing other cations. [ABSTRACT FROM AUTHOR]

In this paper, the existence and multiplicity of solutions of three-point p- Laplacian boundary value problems at resonance with onesided Nagumo condition are studied by using degree theory and upper and lower solutions method. Some known results are improved. [ABSTRACT FROM AUTHOR]