Solvability of a nonlinear second order m-point boundary value problem with p-Laplacian at resonance
Solvability of a nonlinear second order m-point boundary value problem with p-Laplacian at resonance
Abstract We study the existence of solutions of the nonlinear second order m -point boundary value problem with p -Laplacian at resonance $$ \textstyle\begin{cases} (\phi _{p}(x'))'=f(t,x,x'),\quad t\in [0,1],\\ x'(0)=0, \qquad x(1)=\sum_{i=1}^{m-2}a_{i}x(\xi _{i}), \end{cases} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtable> <mml:mtr> <mml:mtd> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>(</mml:mo> <mml:msup> …