Multiple symmetric positive solutions to four-point boundary-value problems of differential systems with \(p\)-Laplacian. (English) Zbl 1261.34023
Summary: We study the four-point boundary-value problem with the one-dimensional \(p\)-Laplacian
\[
(\phi_{p_i}(u_i'))'+q_i(t)f_i(t,u_1,u_2)=0,\quad t\in(0,1),\;i=1,2,
\]
\[ u_i(0)-g_i(u_i'(\xi))=0,\;u_i(1)+g_i(u_i'(\eta))=0, \quad i=1,2. \] We obtain sufficient conditions such that by means of a fixed point theorem on a cone, there exist multiple symmetric positive solutions to the above boundary-value problem. We give an example that illustrates our results.
\[ u_i(0)-g_i(u_i'(\xi))=0,\;u_i(1)+g_i(u_i'(\eta))=0, \quad i=1,2. \] We obtain sufficient conditions such that by means of a fixed point theorem on a cone, there exist multiple symmetric positive solutions to the above boundary-value problem. We give an example that illustrates our results.
MSC:
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
