【摘要】 本文在自反Banach空间中讨论了变分不等式及相应的偏微分方程非齐次边值问题解的存在性.利用非强制条件下变分不等式解的存在性理论,在Sobolev空间中具体地研究了含P-拉普拉斯算子的非线性方程非齐次边值问题解的存在问题.得到了几类非齐次边值问题解的存在条件,去掉了某些不必要的限制,使得适用的范围更为广泛.更多还原

【Abstract】 In reflexive Banach space, the existence of solution of partial differential equation non homogeneous boundary value problems corresponding the variational inequalities is discussed. Applying the existence of solution of variational inequalities under non coercive conditions, we have concretely researched the existence of solution of nonlinear equations non homogeneous boundary value problems involving P Laplacian operator. Some existent conditions of solution of a few non homogeneous boundary value problems are obtained, removing some unnecessary restrictions. The scope of application is wide.更多还原