

Seminar on nonlinear problems of partial differential equations and mathematical physics
February 14, 2023 18:00, Moscow






On elliptic equations with subhomogeneous indefinite nonlinearity
V. Bobkov^{} ^{} Institute of Mathematics with Computing Centre, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa

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Abstract:
We will discuss the existence and multiplicity, as well as some qualitative properties of nonnegative solutions of the zero Dirichlet problem for the quasilinear equation
$$\Delta_p u  \lambda u^{p1} = a(x) u^{q1} $$
in a bounded domain, where $1<q<p$ and the function $a(x)$ is signchanging. A distinctive feature of this
problem is the fact that its nonnegative solutions do not necessarily satisfy the strong maximum principle.
As a consequence, the set of solutions might have a rich structure. We will show, in particular, that for some
$p \neq 2$ there are nontrivial effects which are impossible in the linear case $p=2$.
Website:
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