Maximal Positive Boundary Value Problems as Limits of Singular Perturbation Problems

Exterior Boundary Value Problems as Limits of Interface Problems

It is proved that the solution to exterior Neumann boundary value problem can be obtained as the limit of the solutions of some problems in the whole space. 1 Consider the following problem: (V' + k*)u =f in f2, ul,=O, where f2 = R3\D. D is bounded domain with a smooth boundary r, fE C,(Q), k > 0. In [l] we proved the following: THEOREM 1. Consider the problem V=N in D N = const. > 0. =0 in Q, ...

Positive Solutions for a Class of Singular Boundary-value Problems

Using regularization and the sub-super solutions method, this note shows the existence of positive solutions for singular differential equation subject to four-point boundary conditions.

Positive Solutions for a Class of Singular Boundary-value Problems

This paper concerns the existence and multiplicity of positive solutions for Sturm-Liouville boundary-value problems. We use fixed point theorems and the sub-super solutions method to two solutions to the problem studied. Introduction Consider the boundary-value problem Lu = λf(t, u), 0 < t < 1 αu(0)− βu′(0) = 0, γu(1) + δu′(1) = 0, (0.1) where Lu = −(ru′)′ + qu, r, q ∈ C[0, 1] with r > 0, q ≥ ...

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems

Positive Symmetric Solutions of Singular Semipositone Boundary Value Problems

Using the method of upper and lower solutions, we prove that the singular boundary value problem, −u = f(u) u in (0, 1), u(0) = 0 = u(1) , has a positive solution when 0 < α < 1 and f : R → R is an appropriate nonlinearity that is bounded below; in particular, we allow f to satisfy the semipositone condition f(0) < 0. The main difficulty of this approach is obtaining a positive subsolution, whi...