2021/09/21 by Jarosław Mederski, Alessio Pomponio, Mederski, Jarosław +1 · 1 citation
Computer Science · Mathematics · #35A15 #35J25 #35J93 #35Q75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2109.10155
openalex publication_date 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, using variational methods, we look for non-trivial solutions for the following problem \begincases -\rm div(a(|∇ u|2)∇ u)=g(u), amp; \hboxin ℝN, N≥ 3,
u(x)→ 0, amp;\hboxas |x|→ +∞, \endcases under general assumptions on the continuous nonlinearity g. We assume only growth conditions of g at 0, however no growth conditions at infinity are imposed. If a(s)=(1-s)-1/2, we obtain the well-known Born-Infeld operator, but we are able to study also a general class of a such that a(s)→+∞ as s→ 1-. We find a radial solution to the problem with finite energy.