Stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain

In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in $\mathbb{R}^n$ $$\left\{\begin{aligned} &\frac{\partial^3}{\partial x^3}u(x,y)+\frac{\partial}{\partial x}f(u(x,y))=D_x^{-1}\Delta_yu(x,y),\ \text{in}\ \Omega,\\ &D_x^{-1}u|_{\partial\Omega}=0,\ u|_{\partial\Omega}=0, \end{aligned}\right.$$ where $\Omega\in \mathbb{R}^n$ is a bounded domain with smooth boundary $\partial\Omega$. We utilize critical point theory to establish our main results

Positive Solutions for a System of Discrete Boundary Value Problem

Abstract. This paper deals with the existence and multiplicity of positive solutions for a system of second-order discrete boundary value problem. The main results are obtained via Jensen's inequalities, properties of concave and convex functions and the Krasnosel'skii-Zabreiko fixed point theorem. Furthermore, concave and convex functions are employed to emphasize the coupling behaviors of nonlinear terms f and g and we provide two explicit examples to illustrate our main results and the coupling behaviors

Control of protein activities by conjugation of stimuli-responsive polymers to proteins

Thesis (Ph. D.)--University of Washington, 2000Streptavidin binds biotin with an extraordinary affinity (Ka = 1013--15 M-1). This unique property has found widespread applications in biotechnology fields. However, its application in affinity separation is limited because harsh conditions, which may denature bioactive substances, are required to dissociate biotin from streptavidin.It was the objective of this project to control streptavidin's biotin-binding activity via mild stimulus. In order to induce streptavidin to release bound biotin with mild environmental changes without jeopardizing the extremely high binding affinity, a temperature sensitive polymer, poly(N-isopropylacrylamide) (PNIPAAm) or poly(N,N-diethylacrylamide), was conjugated to a genetically engineered streptavidin in a site-specific manner. The conjugate binds biotin at 4°C, where the polymer is hydrated, and releases a significant fraction of bound biotin at 37°C, where the polymer is collapsed. The binding and release of biotin is reversible. By combining temperature cycling between 4°C and 37°C with washing at 37°C, all of the bound biotin can be released.In contrast to the binding of biotin, the binding of biotinylated bovine serum albumin to the streptavidin-polymer conjugate is shielded at low temperature and enabled at high temperature. The degree of shielding is temperature-sensitive and closely resembles the thermal-responsiveness of the conjugated polymer. The shielding activity is dependent on the size of the target molecules and that of the conjugated polymer. It is shown that the shielding activity of the conjugates is a consequence of the steric effects of the conjugated polymer.PNIPAAm was also conjugated to trypsin to turn on and off the enzymatic activity and to recover the enzyme by thermally induced precipitating. The active center of the conjugate is accessible to both small and large substrates. Surprisingly, the soluble conjugate has higher catalytic activity than native trypsin. Also investigated was the effect of the degree of conjugation on enzymatic activity and on thermal-stability of the conjugate.The technology developed in this research can be applied to other bioactive molecules to control their activities via mild changes in temperature. The streptavidin-polymer conjugate can be used in affinity separations and other fields, such as streptavidin-biotin based immunotherapy, biosensors, tissue engineering, etc