Positive solutions of singular boundary value problems with indefinite weight

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

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 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 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...