Multiplicity and Bifurcation Results for a Class of Quasilinear Elliptic Problems with Quadratic Growth on the Gradient

Rendón F.; Soares M. · Bulletin of the Brazilian Mathematical Society (2025) · DOI: 10.1007/s00574-025-00459-2

Resumen

We investigate the existence, non-existence, and multiplicity of solutions to the following class of quasilinear elliptic equations (Figure presented.) where Ω⊂Rn, n≥3, is a bounded domain with a low-regularity boundary ∂Ω. The coefficients c,h∈Lp(Ω) for some p>n, with c±≥0 and cλ(x):=λc+(x)-c-(x) for a real parameter λ. The matrix A(x) is uniformly positive definite and bounded, while M(x) is positive definite and bounded. Under suitable assumptions, we characterize the solution continuum of (Pλ), including its bifurcation points. We establish existence and uniqueness results in the coercive case (λ≤0) and prove multiplicity results in the non-coercive case (λ>0). © The Author(s), under exclusive licence to Brazilian Mathematical Society 2025.

Instituciones: Universidad Continental