Existence of Solutions for SemilinearIntegro-differential Equations of p-Kirchhoff Type

Author(s)

Existence of Solutions for SemilinearIntegro-differential Equations of p-Kirchhoff Type Eugenio Cabanillas Lapa

In our research we will study the existence of weak solutions to the problem−[M(‖u‖p1,p)]p−1∆pu=f(x,u) +∫Ωk(x,y)H(u)dyin Ω,with zero Dirichlet boundary condition on a bounded smooth domain ofRn,1< p < N;M,f,kandHare given functions. By means of the Galerkin methodand using of the Brouwer Fixed Point theorem we get our results. The uniquenessof a weak solution is also considered.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/103 Armenian Journal of Mathematics, 6(2) 53-63

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Keywords

p-Kirchhoff type equations; variational methods; boundary value problems

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