On Elliptic equations with singular potentials and nonlinear boundary conditions

• Autor(a) principal: Ferreira, Lucas C.F.
• Data de Publicação: 2018
• Outros Autores: Neves, Sérgio L.N. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1090/qam/1506; http://hdl.handle.net/11449/188205
• topic: Elliptic equations; Existence and nonexistence problems; Nonlinear boundary conditions; Singular potentials

We consider the Laplace equation in the half-space satisfying a nonlinear Neumann condition with boundary potential. This class of problems appears in a number of mathematical and physics contexts and is linked to fractional dissipation problems. Here the boundary potential and nonlinearity are singular and of power-type, respectively. Depending on the degree of singularity of potentials, first we show a nonexistence result of positive solutions in D1,2(ℝ+ n) with a Lp-type integrability condition on ∂ℝ+ n. After, considering critical nonlinearities and conditions on the size and sign of potentials, we obtain the existence of positive solutions by means of minimization techniques and perturbation methods.