Positive solutions of a nonlinear impulsive equation with periodic boundary conditions
The author considers the boundary value problem \[ -(p(x)y')' + q(x)y = f(x,y), \quad x \in [a,c)\cup(c,b], \] \[ y(c^-) = d_1y(c^+), \quad (py')(c^-) = d_2(py')(c^+), \] \[ y(a) = y(b),\quad (py')(a) = (py')(b), \] where \(a < c < b\), \(p\), \(q\) are measurable functions, \(f : [a,b]\times {\mathbb R} \to {\mathbb R}\), \(d_1\), \(d_2 \not= 0\). Using various well-known fixed point theorems, several existence (and uniqueness) results for a positive solution to the BVP are obtained.
scientific article; zbMATH DE number 5798104
scientific article