Positive Solutions of Two-point right focal boundary value problems on time scales

AbstractWe consider the following boundary value problem,(−1)n−1yΔn(t)=(−1)p+1F(t,y(σn−1(t))),t∈[a,b]∩T,yΔi(a)=0,0≤i≤p−1,yΔi(σ(b))=0,p≤i≤n−1,where n ≥ 2, 1 ⩽ p ⩽ n - 1 is fixed and T is a time scale. Criteria for the existence of single, double, and multiple positive solutions of the boundary value problem are developed. Upper and lower bounds for these positive solutions are established for two special cases that arise from some physical phenomena. We also include several examples to illustrate the usefulness of the results obtained

Positive Solutions of Two-Point Right Focal Eigenvalue Problems on Time Scales

We offer criteria for the existence of positive solutions for two-point right focal eigenvalue problems (−1)n−pyΔn(t)=λf(t,y(Ãn−1(t)),yΔ(Ãn−2(t)),…,yΔp−1(Ãn−p(t))), t∈[0,1]∩T,yΔi(0)=0, 0≤i≤p−1,yΔi(Ã(1))=0, p≤i≤n−1, where λ>0, n≥2,1≤p≤n−1 are fixed and T is a time scale

Positive Solutions of Two-Point Right Focal Eigenvalue Problems on Time Scales

<p/> <p>We offer criteria for the existence of positive solutions for two-point right focal eigenvalue problems <inline-formula><graphic file="1687-1847-2007-087818-i1.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2007-087818-i2.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2007-087818-i3.gif"/></inline-formula> where <inline-formula><graphic file="1687-1847-2007-087818-i4.gif"/></inline-formula> are fixed and <inline-formula><graphic file="1687-1847-2007-087818-i5.gif"/></inline-formula> is a time scale.</p