singular three-point boundary value problems
Existence theorems for three-point boundary value problem
Basing on a nonlinear alternative, sufficient conditions for the existence of solutions are obtained for the singular boundary value problem NEWLINE\[NEWLINE(\varphi(y'))'= q(x) f(x,y,y'),\quad 0< x< 1,\quad y(0)= A,\quad y(\eta)- y(1)= (\eta- 1)B.NEWLINE\]NEWLINE Here, \(\varphi\) is strictly increasing, \(q\) is positive on \((0,1)\) and integrable. The functions \(\varphi\), \(q\), \(f\) are continuous. The numbers \(\eta\in (0,1)\), \(A\), \(B\) are given. The solution \(y\) is continuously differentiable on \([0,1]\) with \((\varphi(y'))'\) continuous on \((0,1)\).
scientific article; zbMATH DE number 1659052