Affiliation:
1. Chelyabinsk State University
2. Saint Petersburg State University
Abstract
In a bounded domain $\Omega\subset \mathbb{R}^n$, a class of quasilinear elliptic type boundary problems with parameter and
discontinuous nonlinearity is studied.
This class of problems includes the H. J. Kuiper conductor heating problem in a homogeneous electric field.
The topological method is applied to verify the existence of a continuum of generalized positive solutions
from the Sobolev space $W_p^2(\Omega)$ ($p>n$) connecting $(0,0)$ with $\infty$
in the space $\mathbb R\times C^{1,\alpha}(\overline\Omega)$, $\alpha\in (0,(p-n)/p)$. A sufficient condition
for semiregularity of generalized solutions of this problem is given.
The constraints on the discontinuous nonlinearity
are relaxed in comparison with those used by H. J. Kuiper and K. C. Chang.
Funder
Russian Foundation for Basic Research
Publisher
Steklov Mathematical Institute