A non-resonant generalized multi-point boundary-value problem of Dirichelet type involving a p-laplacian type operator

Abstract

We study the existence of solutions for the generalized multi-point boundary-value problem $$displaylines{ (phi (x'))'=f(t,x,x')+equad 0<t<1, cr x(0)=sum_{i=1}^{m-2}a_ix(xi _i),quad x(1)=sum_{j=1}^{n-2}b_jx(au _j), }$$ in the non-resonance case. Our methods consist in using topological degree and some a priori estimates.

Keywords

• Generalized multi-point boundary value problems
• p-Laplace type operator
• non-resonance
• a priori estimates
• topological degree.