In this work, we study the existence of the principal eigencurves for a Steklov problem with an indefinite weight for homogeneous perturbation of the p-Laplacian operator. We then establish many properties of these eigencurves: continuity, differentiability and asymptotic behaviors. We also use our approach to get similar result when mixed Dirichlet-Steklov boundary condition is considered.

We use the steepest descent method in an Orlicz–Wasserstein space to study the existence of solutions for a very broad class of kinetic equations, which include the Boltzmann equation, the Vlasov–Poisson equation, the porous medium equation, and the parabolic p-Laplacian equation, among others. We combine a splitting technique along with an iterative variational scheme to build a discrete solution which converges to a weak solution of our problem.

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