论文标题
关于涉及1-Laplacian操作员和不连续的非线性的准椭圆形问题
On a quasilinear elliptic problem involving the 1-laplacian operator and a discontinuous nonlinearity
论文作者
论文摘要
在这项工作中，我们研究了涉及1-拉普拉斯操作员的准椭圆形问题，该问题具有不连续的，超线性和亚临界非线性，涉及重质函数$ h（\ cdot -β）$。我们的方法基于对相关的P拉普拉斯问题的分析，然后对渐近行为或诸如$ p \至1^+$之类的解决方案进行彻底分析。我们还研究了解决方案的渐近行为，即$β\至0^+$，我们证明它会收敛到原始问题的溶液，而没有非线性不连续性。
In this work, we study a quasilinear elliptic problem involving the 1-laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function $H(\cdot - β)$. Our approach is based on an analysis of the associated p-laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as $p \to 1^+$. We study also the asymptotic behaviour of the solutions, as $β\to 0^+$ and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.
