Eigenvalues of $ -Delta_p -Delta_q $ Under Neumann Boundary Condition

Canadian mathematical bulletin

Mihai Mihăilescu¹  Gheorghe Moroşanu² 

[1] Department of Mathematics, University of Craiova, 200585 Craiova, Romania;Department of Mathematics and its Applications, Central European University, 1051 Budapest, Hungary

关键词: eigenvalue problem;    Sobolev space;    Nehari manifold;    variational methods;   

DOI  :  10.4153/CMB-2016-025-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Theeigenvalue problem $-Delta_p u-Delta_q u=lambda|u|^{q-2}u$with $pin(1,infty)$, $qin(2,infty)$, $peq q$ subject tothecorresponding homogeneous Neumann boundary condition isinvestigated on a bounded open set with smooth boundary from$mathbb{R}^N$ with $Ngeq 2$. A careful analysis of this problem leadsus to a complete description of the set of eigenvalues as beingaprecise interval $(lambda_1, +infty )$ plus an isolated point$lambda =0$. This comprehensive result is strongly related toourframework which is complementary to the well-known case $p=qeq2$ for which a full description of the set of eigenvalues isstillunavailable.

【 授权许可】

Unknown