In this article we establish the existence of at least two distinct solutions to singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions.

In this paper, we study the multiplicity of positive solutions for the p-Laplacian problems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic equation has at least two positive solutions.

We examine the question of how the ranking between di erent distributions with respect to a one-parameter family of weight functions depend on the parameter. We argue that in this context sign regularity of the family of weight functions is a natural condition to consider. Several classical economical examples are shown to satisfy this condition. We use sign regularity to obtain results on the ...

this paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎with the help of the nehari manifold and palais-smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a certai...