Infinitely Many Regular Weak Solutions for Odd Symmetric Prescribed Mean Curvature Problems

We establish the existence of infinitely many regular weak solutions of the prescribed mean curvature problem -div (del u/root 1 + |del u|(2)) = f (x, u) in Omega, Bu = 0 on partial derivative Omega, where Omega is a bounded domain in R-N, with a regular boundary partial derivative Omega, B is either the Dirichlet, or the Neumann, or the mixed boundary operator, the function f (x, s) is odd with respect to s is an element of R and has a potential F(x, s) = integral(s)(0) f (x, t) dt, which is desultorily subquadratic at s = 0, locally with respect to x is an element of Omega. Our findings improve and extend in various directions the previous results obtained in the literature.

Automated summary

We establish the existence of infinitely many regular weak solutions for the prescribed mean curvature problem in a bounded domain Omega in R-N. The functions f(x,s) and F(x,s) are odd with respect to s and have certain properties. Our findings improve and expand upon previous results in the literature.