Método de Nehari e aplicações

Abstract

In this work, we use the Nehari Method to show the existence of a Ground State solution for the following boundary value problem based in [9]...where Ω ⊂ R N denotes a bounded domain, ∆ is the Laplacian operator, and the nonlinearity f ∈ C1(R, R) satisfies suitable regularity and growth hypotheses, such as...for constants C > 0 and 2 < r < 2∗, where 2 ∗represents the critical Hardy-Sobolev exponent with value...We also apply Nehari’s Method to prove the existence of a nodal solution with minimum energy for the Kirchhoff-type problem proposed in [10] and described by where Ω ⊂ R3 is a smooth and bounded domain, and it is assumed that the nonlinearity f, as well as the nonlocal term M, satisfy adequate regularity and growth hypotheses.