Author:
Leuyacc Yony Raúl Santaria
Abstract
<abstract><p>In this work, we are interested in studying the existence of nontrivial weak solutions to the following class of Schrödinger equations</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left\lbrace\begin{array}{rcll} -{\rm div}(w(x)\nabla u) \ & = &\ f(x, u), &\ x \in B_1(0), \\ u \ & = &\ 0, &\ x \in \partial B_1(0), \end{array}\right. $\end{document} </tex-math></disp-formula></p>
<p>where $ w(x) = \big(\ln (1/|x|)\big)^{\beta} $ for some $ \beta \in [0, 1) $, the nonlinearity $ f(x, s) $ behaves like $ {\rm \exp}((1+h(|x|))|s|^{2/(1-\beta)}) $ and $ h $ is a continuous radial function such that $ h(r) $ tends to infinity as $ r $ tends to $ 1 $. The proof involves variational methods and a new version of Trudinger-Moser inequality.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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