This paper examines a class of Kirchhoff type equations that involve sign-changing weight functions. Using Nehari manifold and fibering map, the existence of multiple positive solutions is established.

No abstract

No abstract

When the Jacobian of a computed numerical solution of a polynomial system in C n allows very small singular values, the solution could be isolated with a multiple multiplicity or may belong to a solution component with positive dimension. The algorithm constructed in this article intends to differentiate those cases by determining the dimension of the solution component M in which the solution lies. Of particular interest is the case when dim(M) = 0, then the solution is of course isolated. While the proposed algorithm is experimental, it has been tested successfully on the class of problems with the solution in question belonging to a reduced component. Numerical results are provided to illustrate the accuracy of the algorithm.

No abstract