Positive solutions and nonlinear multipoint conjugate eigenvalue problems

• Main Authors: Paul W. Eloe, Johnny Henderson
• Format: Article
• Language: English
• Published: Texas State University 1997-01-01
• Series: Electronic Journal of Differential Equations
• Subjects: multipoint; nonlinear eigenvalue problem; cone.
• Online Access: http://ejde.math.txstate.edu/Volumes/1997/03/abstr.html

Values of $lambda$ are determined for which there exist solutions in a cone of the $n^{th}$ order nonlinear differential equation, $$u^{(n)} = lambda a(t) f(u),,quad 0 < t < 1,,$$ satisfying the multipoint boundary conditions, $$u^{(j)}(a_i) = 0,,quad 0leq jleq n_i -1,,quad 1 leq i leq k,,$$ where $0 = a_1 < a_2 < cdots < a_k = 1$, and $sum _{i=1}^k n_i = n$, where $a$ and $f$ are nonnegative valued, and where both $limlimits_{|x| o 0^+} f(x)/|x|$ and $limlimits_{|x| oinfty} f(x)/|x|$ exist.