Three Symmetric Positive Solutions for Lidstone Problems by a Generalization of the Leggett-Williams Theorem
Avery, Richard I.
Davis, John M.
Southwest Texas State University, Department of Mathematics
We study the existence of solutions to the fourth order Lidstone boundary value problem y(4)(t) = ƒ(y(t), -y" (t)), y(0) = y"(0) = y"(1) = y(1) = 0. By imposing growth conditions on ƒ and using a generalization of the multiple fixed point theorem by Leggett and Williams, we show the existence of at least three symmetric positive solutions. We also prove analogous results for difference equations.
Lidstone boundary value problem, Green's function, Multiple solutions, Fixed points, Difference equation
Avery, R. I., Davis, J. M., & Henderson, J. (2000). Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem. <i>Electronic Journal of Differential Equations, 2000</i>(40), pp. 1-15.