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.

In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign-changing weight function. With the help of the Nehari manifold, we prove that there are at least two positive solutions for Eq. (E λ,f ) in bounded domains.

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In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (E λ,μ ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (λ, μ) belongs to a certain subset of R 2 .

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