| Full text | |
| Author(s): |
Pimenta, Marcos T. O.
;
Winkert, Patrick
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Annali di Matematica Pura ed Applicata; v. N/A, p. 17-pg., 2025-03-25. |
| Abstract | |
In this paper we study strongly singular problems with Dirichlet boundary condition on bounded domains given by<br /> -div (Vul Vu+ (x) VuVu) h(x) (+) in Omega,<br /> where I <p< N. p 0 <euro> L (2), 1 <r and te L(2) with hix) 0 for aa.. 2. Since the exponent r is larger than one, the corresponding energy functional is not continuous anymore and so the related Nehari manifold N={u is an element of W1,H0():& Vert;del u & Vert;pp+& Vert;del u & Vert;qq,mu-integral h(x)(u+)1-rdx=0}<br /> is not closed in the Musiclak-Orlicz Sobolev space w. (2). Instead we are minimizing the<br /> energy functional over the constraint set<br /> M={u is an element of W-0(1,H)(Omega):& Vert;del u & Vert;pp+& Vert;del u & Vert;qq,mu-integral h(x)(u+)1-rdx >= 0},<br /> which turns out to be closed in W (2) and prove the existence of at least one weak solution. Our result is even new in the case when the weight function a is away from zero. (AU) | |
| FAPESP's process: | 23/05300-4 - Elliptic problems involving the (1,q)-laplacian and the double-phase operator |
| Grantee: | Marcos Tadeu de Oliveira Pimenta |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 23/06617-1 - Quasilinear elliptic PDEs involving the (1,q) Laplacian and the double phase operator |
| Grantee: | Marcos Tadeu de Oliveira Pimenta |
| Support Opportunities: | Regular Research Grants |