Existence and Morse Index of least energy nodal solution of the (p,2)-laplacian

2018/12/06 by Agudelo, Oscar, Restrepo, Daniel, Velez, Carlos
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.02389

Abstract

In this paper we study the quasilinear equation - \ep² Δu-Δ_p u=f(u) in a smooth bounded domain Ω with Dirichlet boundary condition. For \ep ≥ 0, we review existence of a least energy nodal solution and then present information about the Morse Index of least nodal energy solutions this BVP. In particular we provide Morse Index information for the case \ep =0.

Related

• Existence and nonexistence of least energy nodal solution for a class of elliptic problem in ℝ²
• Nodal Solutions for sublinear-type problems with Dirichlet boundary\n conditions
• Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane-Emden equation in dimension two
• Entire nodal solutions to the pure critical exponent problem for the p-Laplacian
• A further note on the inverse nodal problem and Ambarzumyan problem for the p-Laplacian