On positive solutions for $(p,q)$-Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We study the existence and non-existence of positive solutions for the $(p,q)$-Laplace equation $-{\Delta }_{p}u-{\Delta }_{q}u=\alpha |u{|}^{p-2}u+\beta |u{|}^{q-2}u$, where $p\ne q$, under the zero Diri…