Nonlinear eigenvalue problems for higher order Lidstone boundary value problems

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 for Higher Order Lidstone Boundary Value Problems. a New Approach via Sperner’s Lemma

Consider the higher order nonlinear scalar differential equations (0.1) x(t) = −f(t, x(t), ..., y(t), ...y(2(n−1))(t)), 0 ≤ t ≤ 1 where f ∈ C([0, 1] × R+, R+), R+ = [0,∞) associated to the Lidstone boundary conditions (0.2) x(0) = 0 = x(1), (0.3) x(0) = 0 = x(1). Existence of a solution of boundary value Problems (BVP) (0.1)-(0.2) such that x(t) > 0, 0 < t < 1, i = 0, 1, ..., n− 1 are given, un...

Boundary value problems for higher order parabolicequationsRussell

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...