(2,p)-Laplace方程的紧性条件及其应用

Compactness Condition of (2,p)-Laplacian Equation and Its Applications

利用变分方法研究带有Dirichlet边界条件的(2,p)-Laplace方程。在非线性项由pLaplace算子的第一特征值刻画时,利用p-Laplace算子的Fucik谱理论得到此方程所对应能量泛函的紧性条件;在非线性项满足两个经典条件时,利用此紧性条件得到此方程正解的存在性。

Using variational methods,the(2,p)-Laplacian equation with the Dirichlet boundary condition was studied.When the nonlinearity is characterized by the first eigenvalue of p-Laplacian operator,the compactness condition of the energy functional corresponding to this equation was obtained.Using this compactness condition,the existence of positive solutions for this equation with the nonlinearity satisfying two classical conditions was obtained.