Positive solutions of singular \((k,n-k)\) conjugate boundary value problem. (English) Zbl 1354.34047
From the introduction and summary: In this paper, we are concerned with positive solutions for singular \((k,n-k)\) conjugate boundary value problem
\[
(-1)^{n-k} y^{(n)}(x)=\lambda h(x) f(y),\qquad 0<x<1,
\]
\[ y^{(i)}(0)= ,\;y^{(j)}(1)= 0,\qquad 0\leq i\leq k-1,\;0\leq j\leq n-k-1, \] where \(1\leq k\leq n-1\) is a positive number and \(\lambda>0\) is a parameter.
The existence of a positive solution is studied by employing a priori estimates, the conce theorem and the fixed index.
\[ y^{(i)}(0)= ,\;y^{(j)}(1)= 0,\qquad 0\leq i\leq k-1,\;0\leq j\leq n-k-1, \] where \(1\leq k\leq n-1\) is a positive number and \(\lambda>0\) is a parameter.
The existence of a positive solution is studied by employing a priori estimates, the conce theorem and the fixed index.
MSC:
34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |