Positive solutions for a class of nonresonant boundary-value problems
Texas State University-San Marcos, Department of Mathematics
This paper concerns the existence and multiplicity of positive solutions to the nonresonant second-order boundary-value problem Lx = λw(t)ƒ(t, x). We are interested in the operator Lx := -x″ + ρqx when w is in Lp for 1 ≤ p ≤ +∞. Our arguments are based on fixed point theorems in a cone and Hölder's inequality. The nonexistence of positive solutions is also studied.
Positive solution, Fixed point theorem, Existence, Complete continuity
Zhang, X. (2007). Positive solutions for a class of nonresonant boundary-value problems. <i>Electronic Journal of Differential Equations, 2007</i>(20), pp. 1-10.