论文标题
渐近上$ Q $ -linear $（P，Q）$的多个解决方案
Multiple solutions for asymptotically $q$-linear $(p,q)$-Laplacian problems
论文作者
论文摘要
我们研究了问题的解决方案的存在和多样性$$ \ begin {case}-Δ_pu -Δ_qu = g（x，x，x，x，x，x，x，x，q，quad＆\ mbox {in}Ω $ \ mathbb r^n $，$ 1 <p <q <\ infty $，而非linearity $ g $的行为为$ u^{q-1} $在无穷大。我们使用变分方法并找到多个溶液作为相关能量功能的最小临界点。在适当的关于非线性的假设下，我们还介绍了共鸣案例。
We investigate the existence and the multiplicity of solutions of the problem $$ \begin{cases} -Δ_p u-Δ_q u = g(x, u)\quad & \mbox{in } Ω,\\ \displaystyle{u=0} & \mbox{on } \partialΩ, \end{cases} $$ where $Ω$ is a smooth, bounded domain of $\mathbb R^N$, $1<p<q<\infty$, and the nonlinearity $g$ behaves as $u^{q-1}$ at infinity. We use variational methods and find multiple solutions as minimax critical points of the associated energy functional. Under suitable assumptions on the nonlinearity, we cover also the resonant case.
