Prescribed elliptical problems, without symmetry in the RN and in unlimited domains: Existence and multiplicity of nodal solutions

• Grant number: 24/04098-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2025
• End date: July 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Olimpio Hiroshi Miyagaki
• Grantee: Carolina Santana Tomaz
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations, AP.TEM

Abstract

This project studies classes of prescribed elliptical problems, without periodicity and symmetry, in relation to the existence and multiplicity of positive and nodal solutions (solutions that change sign). The prototype of the problem is Schrödinger's stationary equation-\Delta u+a(x)u=f(u),u \in H^1(R^N), where 0\leq a \in C(R^N, R), with decay condition, but not symmetric or periodic, f(u)=|u|^{p-2}u, 2