Existence Results for an Elliptic Equation of Kirchhoff-Type with Changing Sign Data

By N. Azzouz, A. Bensedik. 2012

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Let Ω be a bounded domain in RN (N > 2). We are concerned with the existence and nonexistence of solutions for the following nonlocal problem, –M (∫Ω|∇u(x)|2dx)Δu = |u|p–1u + λf(x) in Ω, u|∂Ω = 0. Where M is continuous function on R+ and f ∈ C1($\overline{\Omega}$) changes sign. λ and p are positive parameters. By direct variational method, Galerkin approach and sub and super solutions method some results are established.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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