Abstract
In [1], I. N. Vekua propose the Poincaré problem for some second order elliptic equations, but it can not be solved. In [2], the authors discussed the boundary value problem for nonlinear elliptic equations of second order in some bounded domains. In this article, the Poincaré boundary value problem for general nonlinear elliptic equations of second order in unbounded multiply connected domains have been completely investigated. We first provide the formulation of the above boundary value problem and corresponding modified well posed-ness. Next we obtain the representation theorem and a priori estimates of solutions for the modified problem. Finally by the above estimates of solutions and the Schauder fixed-point theorem, the solvability results of the above Poincaré problem for the nonlinear elliptic equations of second order can be obtained. The above problem possesses many applications in mechanics and physics and so on.
Highlights
We first provide the formulation of the above boundary value problem and corresponding modified well posed-ness
We assume that D is a circular domain in z 1, where the boundary consists of N 1 circles 0 N 1 z 1
In the domain D, find a solution u z of Equation (1.1), which is continuously differentiable in D, and satisfies the boundary condition c1 z u
Summary
By the above estimates of solutions and the Schauder fixed-point theorem, the solvability results of the above Poincaré problem for the nonlinear elliptic equations of second order can be obtained. In the domain D, find a solution u z of Equation (1.1), which is continuously differentiable in D , and satisfies the boundary condition c1 z u Are distinct points, and bj j J 0 are all real constants satisfying the conditions bj k3, j J 0 , (1.10)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
