The effect of domain shape on the number of positive solutions of certain nonlinear equations. II. (English) Zbl 0729.35050

[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.


35J65 Nonlinear boundary value problems for linear elliptic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs


Zbl 0662.34025
Full Text: DOI


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