Existence of solution for Schr "odinger equation with discontinuous\n nonlinearity and critical Growth

2021/11/04 by Geovany F. Patricio, Patricio, Geovany Fernandes
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.03097

openalex publication_date 2021/11/04 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

This paper concerns with the existence of nontrivial solution for the\nfollowing problem \
left

beginaligned -
Delta u + V(x)u amp; =\n
gamma H_e(|u|-a)|u|^q-2u+|u|^2^*-2u
;
;
mbox\nin
;
;
mathbbR^N,
nonumber u
in H¹(
mathbbR^N).
endaligned\n
right. where, N\≥ 3, \γ\≥ 0, H_e:\ℝ \→\n\ℝ denotes the Heaviside function, a \≥ 0, 2<q<2^* and\nV: mathbbR^N \→ \ℝ is \ℤ^N-periodic with \β= 0\ndoes not belong to the spectrum of -\Δ+V.\n

Related

• Non-degeneracy and existence of new solutions for the Schrödinger equations
• New type of solutions for Schrödinger equations with critical growth
• Solutions concentrating around the saddle points of the potential for Schrödinger equations with critical exponential growth
• Normalized solutions for a Schrödinger equation with critical growth in ℝ^N
• On the Schrodinger equation in R^N under the effect of a general nonlinear term