On ΛpBV-Solutions of Some Nonlinear Integral Equations on the Plane

Abstract

In this paper, we define the space of functions ${\mathrm{\Lambda }}_p$-bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, $\left({\mathrm{\Lambda }}_{p}BV\left(I_a^b,\mathrm{ℝ}\right)\right)$.