Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces

This paper investigates the multiplicity of positive solutions for a class of nonlinear boundary-value problems of fourth-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator. The nonexistence of positive solution is also studied. Meanwhile, an example is worked out to demonstrate the main results.     

Exact number of solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian

In this paper, exact number of solutions are obtained for the one-dimensional p-Laplacian in a class of two-point boundary value problems. The interesting point is that the nonlinearity f is general form: f(u)=λg(u)+h(u). Meanwhile, some properties of the solutions are given in details. The arguments are based upon a quadrature method.     

Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions

This paper studies the existence of symmetric positive solutions for a second-order nonlinear ordinary differential equation with integral boundary conditions by applying the theory of fixed point index in cones. For the demonstration of the results, an illustrative example is presented.     

Influence of Vinyl Groups on the UV-Visible Spectra and Self-Dimerization of Pyrromethenones

Spectral analyses of vinylneoxantho- and vinylisoneoxanthobilirubic acid methyl esters, with endo and exo-vinyl groups respectively, show that the exo-vinyl group causes (1) a greater bathochromic and hyperchromic shift of the long wavelength UV-vis absorption and (2) a smaller dimer association constant in CDCl₃ than does the endo-vinyl in these pyrromethenones.     

Triple positive solutions for a class of -point dynamic equations on time scales with -Laplacian

This paper deals with a class of second-order nonlinear m-point dynamic equation on time scales with one-dimensional p-Laplacian. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order delta derivative explicitly. Meanwhile, an example is worked out to demonstrate the main results.     

Hierarchical NiCo2S4 Nanotube@NiCo2S4 Nanosheet Arrays on Ni Foam for High‐Performance Supercapacitors

Hierarchical NiCo₂S₄ nanotube@NiCo₂S₄ nanosheet arrays on Ni foam have been successfully synthesized. Owing to the unique hierarchical structure, enhanced capacitive performance can be attained. A specific capacitance up to 4.38 F cm^?2 is attained at 5 mA cm^?2, which is much higher than the specific capacitance values of NiCo₂O₄ nanosheet arrays, NiCo₂S₄ nanosheet arrays and NiCo₂S₄ nanotube arrays on Ni foam. The hierarchical NiCo₂S₄ nanostructure shows superior cycling stability; after 5000 cycles, the specific capacitance still maintains 3.5 F cm^?2. In addition, through the morphology and crystal structure measurement after cycling stability test, it is found that the NiCo₂S₄ electroactive materials are gradually corroded; however, the NiCo₂S₄ phase can still be well‐maintained. Our results show that hierarchical NiCo₂S₄ nanostructures are suitable electroactive materials for high performance supercapacitors.     

Existence result of second-order differential equations with integral boundary conditions at resonance

By using Mawhin's continuation theorem, some sufficient conditions for the existence of solution for a class of second-order differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case dimKerL=2, which will cause some difficulties in constructing the projector Q. Since all the existence results obtained in previous papers are for the case dimKerL=1, our work is new.