### A class of positive linear operators and applications to nonlinear boundary value problems

#### Abstract

We discuss the class of $u_0$-positive linear operators relative

to two cones and use a comparison theorem for this class to give

some short proofs of new fixed point index results for some nonlinear

operators that arise from boundary value problems. In particular, for

some types of boundary conditions, especially nonlocal ones, we obtain

a new existence result for multiple positive solutions under conditions

which depend solely on the positive eigenvalue of a linear operator.

We also treat some problems where the nonlinearity $f(t,u)$ is singular

at $u=0$.

to two cones and use a comparison theorem for this class to give

some short proofs of new fixed point index results for some nonlinear

operators that arise from boundary value problems. In particular, for

some types of boundary conditions, especially nonlocal ones, we obtain

a new existence result for multiple positive solutions under conditions

which depend solely on the positive eigenvalue of a linear operator.

We also treat some problems where the nonlinearity $f(t,u)$ is singular

at $u=0$.

#### Keywords

Positive linear operator; fixed point index; positive solution; nonlocal boundary value problem

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.