论文标题
可能具有单数非线性的一类非局部问题的积极解决方案
Positive solutions for a class of nonlocal problems with possibly singular nonlinearity
论文作者
论文摘要
我们研究了一类具有均匀dirichlet边界条件的椭圆问题和非线性反应项$ f $，这是非本地的，具体取决于$ l^{p} $ - 未知功能的规范。非线性$ f $可以使问题退化，因为它在非本地变量中甚至可能具有多个奇异性。我们为适当定义的解决方案图使用固定点参数，以产生具有有序规范的经典正面解决方案。
We study a class of elliptic problems with homogeneous Dirichlet boundary condition and a nonlinear reaction term $f$ which is nonlocal depending on the $L^{p}$-norm of the unknown function. The nonlinearity $f$ can make the problem degenerate since it may even have multiple singularities in the nonlocal variable. We use fixed point arguments for an appropriately defined solution map to produce multiplicity of classical positive solutions with ordered norms.
