Quasilinear Differential Equation with Riemann–Liouville Fractional Derivative and Logarithmic Nonlinearity

Nyamoradi N.; Bonilla M.; Rodríguez J.A.; Torres Ledesma C.E. · Lobachevskii Journal of Mathematics (2026) · DOI: 10.1134/s1995080226617200

Resumen

Abstract: In this paper, we study the existence of solutions for a class of -Laplacian equations involving fractional derivatives in the sense of Riemann–Liouville and Caputo, combined with a logarithmic-type nonlinearity. The problem is considered on a bounded interval with homogeneous exterior conditions. The nonlinearity includes a sign-changing weight and a lower-order perturbation depending on a real parameter. The analysis is carried out within a suitable fractional Sobolev framework by means of variational methods, specifically the Nehari manifold and fibering map techniques. Under appropriate assumptions on the parameters and the nonlinear terms, we establish the existence of nontrivial solutions. © Pleiades Publishing, Ltd. 2026.

Instituciones: Universidad Nacional de Trujillo