On 2nth-order Lidstone boundary value problems

Finite spectrum of 2nth order boundary value problems

For any even positive integer 2n and any positive integermwe construct a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most (2n − 1)m + 1 eigenvalues. Our main result reduces to previously known results for the cases n = 1 and n = 2. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n(m + 1)...

Complementary Lidstone Interpolation and Boundary Value Problems

1 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA 2 Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3 Department of Mathematics, Azores University, R. Mãe de Deus, 9500-321 Ponta Delgada, Portugal 4 School of ELectrical & Electronic Engineering, Nanyang Technological University, Sin...

Eigenvalues of complementary Lidstone boundary value problems

where l > 0. The values of l are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of l such that for any l in the interval, the existence of a positive solution of the boundary value problem is guaranteed. Some examples are also included to illustrate the results obtained. Note that the nonlinear term F depends on y’ and this deriv...

Existence and Local Uniqueness for Nonlinear Lidstone Boundary Value Problems

Higher order upper and lower solutions are used to establish the existence and local uniqueness of solutions to y = f(t, y, y′′, . . . , y(2n−2)), satisfying boundary conditions of the form gi(y(0), y(2i−2)(1))−y(2i−2)(0) = 0, hi(y(0), y(2i−2)(1))−y(2i−2)(0) = 0, 1 ≤ i ≤ n.

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems