Existence of solutions for nonlinear equations with mixed local and nonlocal operators

Puntos clave

• The aim is to establish the existence of solutions for an elliptic equation influenced by mixed local and nonlocal operators.
• Studied an elliptic equation with homogeneous Dirichlet boundary conditions.
• Utilized a mixed type operator combining the Laplacian and fractional Laplacian.
• Applied a critical point theorem for proof of existence.
• Considered a parametric reaction and an undetermined source term.
• Established existence of at least one solution for specific source conditions.
• Conditions depend on the choice of parameters being sufficiently small.