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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
$$-\Delta_p u - \lambda u^{p-1} = a(x) u^{q-1} $$
in a bounded domain, where $1<q<p$ and the function $a(x)$ is sign-changing. 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: https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%2266c4b047-af30-41c8-9097-2039bac83cbc%22%7d
 
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