The effect of domain shape on the number of positive solutions of certain nonlinear equations. II (Q805890)

[For part I see ibid. 74, No.1, 120-156 (1988; Zbl 0662.34025).] This paper is a continuation of part I. The author deals with the problem \[ (*)\quad -\Delta u=\lambda f(u)\text{ in } \Omega \subset {\mathbb{R}}^ m;\quad u=0\text{ on } \partial \Omega. \] Changing the domain, he studies the number of positive solutions to the problem (*). If \(\Omega\) is star-shaped then the equation (*) has many solutions. In some cases the positive solutions are not connected. Next, using the same technic as in part I the author proves some results for a non-selfadjoint problem, for the Neumann boundary value problem and for the parabolic problem.