Existence of Nodal solutions of boundary value problems with two multi-point boundary conditions. (English) Zbl 1312.34052
Summary: We study the nonlinear boundary value problem consisting of the equation
\[
y''+ w(t)f(y)= 0\quad\text{on }[a, b]
\]
and the multi-point boundary condition
\[
y'(a)- \sum^l_{j=1} h_jy'(\xi_j)= 0,\quad y'(b)- \sum^m_{i=1} k_i y'(\eta_i)= 0.
\]
We establish the existence of various nodal solutions by matching the solutions of two boundary value problems at some point in \((a,b)\), each of which involves one separated boundary condition and one multi-point boundary condition. We also obtain conditions under which this problem does not have certain types of nodal solutions.
MSC:
34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |