Boundedness of green operators for nonlocal equations on weighted lebesgue spaces

Abstract

In this research. we establish the local existence and uniqueness of solutions for the Cauchy problem of the nonlocal equation of the form ∂ₜU(x.t) = ∫R n J(x.Y)U(Y,t)dY – U (x.t) + (In(e + I x I2)) U p (x,t) where p > 1 and ∂ > 0 are constants. In this research, the kernel / of the nonlocal term may not radially symmetric. We investigate the Cauchy problem on weighted Lebesgue spaces with a logarithmic weight. One of the most important results in this thesis is the boundedness of the corresponding Green operator on the weight Lebesgue spaces. We also establish the local well-poseduess of the problem.