Soluções estacionárias positivas de equações de primeira ordem com termo de Kirchhoff e falta de coercitividade

Abstract

In this work, we investigate the existence of positive stationary solutions of the Kirchhoff equations in a limited domain, an inhomogeneous spatial coefficient and a function of first order terms with growth up to the natural. Unlike the coercive cases where the operator has a suitable lower-order term or a Dirichlet boundary condition, in the case of a refreshing Neumann boundary condition, a lack of coercivity in the Kirchhoff term occurs. In this last scenario, we prove an existence result that plays the role of a sub-supersolution principle for positive solutions of. As an application, examples are provided that show the existence of positive stationary solutions satisfying the Neumann boundary condition. To overcome the lack of coercivity we combine monotonicity and truncation techniques, with the theory of elliptic regularity, in order to construct parametric approximate problems that are coercive, and whose solutions converge, as the parameter tends to zero, to a solution.