Structure Of Solutions For Equations Research Articles

The structure of solutions for equations related to the motions of plane curves

AbstractWe study the structure of solutions of an initial value problem arising in the study of steadily rotating spiral waves in the kinematic theory of excitable media. In particular, we prove that under certain conditions there is a unique global positive monotone increasing solution.

Global structure of solutions for equations of Brezis–Nirenberg type on the unit ball

The Brezis–Nirenberg equation and the scalar field equation on the three-dimensional unit ball are studied. Under the Robin condition, we show the existence and uniqueness of radial solutions in a unified way. In particular, it is shown that the global structure of solutions changes qualitatively when a parameter in the boundary condition exceeds a certain critical value.

Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball

The Brezis-Nirenberg equation and the scalar field equation on the three-dimensional unit ball are studied. Under the Robin condition, we show the existence and uniqueness of radial solutions in a unified way. In particular, it is shown that the global structure of solutions changes qualitatively when a parameter in the boundary condition exceeds a certain critical value.