arXiv subjects
Publications and source records attributed to Jinxiu Mao.
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
This paper studies Laplace's equation $-Δ\,u=0$ in an exterior region $U\varsubsetneq{\mathbb R}^N$, when $N\geq3$, subject to the nonlinear boundary condition $\frac{\partial u}{\partialν}=λ{\left\vert{u}\right\vert}^{q-2}u+μ{\left\vert{u}\right\vert}^{p-2}u$ on $\partial U$ with $1 0$ and $μ\in\mathbb R$ arbitrary, then there exists a sequence $\left\{u_k\right\}$ of solutions with negative energy converging to $0$ as $k\to\infty$; on the other hand, when $λ\in\mathbb R$ and $μ>0$ arbitrary, then there exists a sequence $\left\{\tilde{u}_k\right\}$ of solutions with positive and unbounded energy. Also, associated with the $p$-Laplacian equation $-Δ_p\,u=0$, the exterior $p$-harmonic Steklov eigenvalue problems are described.