论文标题
一维非本地SINH-POISSON方程的签名解决方案
Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation
论文作者
论文摘要
我们在$ i $的外部条件下，在有限的一维间隔$ i $下，研究了一个非本地版本的Sinh-Poisson方程的签名解决方案的存在。该模型与简单电化学系统的电腐蚀现象的数学描述严格相关。通过有限维的Lyapunov-Schmidt减少方法，我们构建了起泡的解决方案家族，开发了任意规定的数字标记峰值。通过仔细分析解决方案的极限曲线，我们还表明，节点区域的数量与爆破点的数量一致。
We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval $I$, under Dirichlet conditions in the exterior of $I$. This model is strictly related to the mathematical description of galvanic corrosion phenomena for simple electrochemical systems. By means of the finite-dimensional Lyapunov-Schmidt reduction method, we construct bubbling families of solutions developing an arbitrarily prescribed number sign-alternating peaks. With a careful analysis of the limit profile of the solutions, we also show that the number of nodal regions coincides with the number of blow-up points.
