A numerically based investigation on the symmetry breaking and asymptotic behavior of the ground states to the -Hénon equation.
We consider the existence of positive solutions of the singular nonlinear semipositone problem of the form where is a bounded smooth domain of with , , , , and , , and are positive parameters. Here is a continuous function. This model arises in the studies of population biology of one species with representing the concentration of the species. We discuss the existence of a positive solution when satisfies certain additional conditions. We use the method of sub-supersolutions...
We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.
In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.