Existence results for a class of Kirchhoff type systems with Caffarelli-Kohn-Nirenberg exponents

Abstract

This paper is concerned with the existence of positive solutions for a class of infinite semipositone kirchhoff type systems with singular weights. Our aim is to establish the existence of positive solution for λ large enough. The arguments rely on the method of sub-and super-solutions.

Positive Solution for a Class of Nonlocal Elliptic System With Multiple Parameters and Singular Weights

“…A key role in our arguments will be played by the following auxiliary result. Its proof is similar to those presented in [12], the reader can consult further the papers [1,2,3,18].…”

“…So, the study of positive solutions of elliptic systems has more practical meanings. We refer to [1,2,3,4,5,6,8,17] for additional results on elliptic problems. We are inspired by the ideas introduced in many papers such as [2,4,13,24], to establish the existence of a positive weak solution for (1.1) by using sub-and supersolutions method.…”

Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities

“…Meanwhile, the problem about Kirchhoff system has been studied. In [16,17] the Kirchhoff system with boundary value shows several physical and biological systems with u and v describing a process depending on the average of itself, such as population densities. Lv and Peng [18] established the existence of positive vector solutions and positive vector ground state solutions by using variational methods and also studied the asymptotic behavior of these solutions.…”