Special Session 93: Local and nonlocal elliptic boundary value problems

Multiple positive solutions for quasilinear nonlocal problem via topological, variational and set-valued methods
Leszek Gasinski
University of the National Education Commission
Poland
Co-Author(s):    
Abstract:
We study a nonlocal quasilinear problem driven by the p-Laplacian operator of a nonvariational type, without assuming any kind of monotonicity on the data. The nonlocal term depends on the L^q-norm of the unknown function, where p and q are independent exponents and the weight function can be sign changing. The multiplicity of positive solutions is established through a combination of variational methods, truncation techniques, set-valued analysis, and fixed-point results.