Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Positive solutions for nonlinear systems of third-order generalized sturm-liouville boundary value problems with $(p_1,p_2,ldots,p_n)$-laplacian

In this work, byemploying the Leggett-Williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-Laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

Positive Solutions for Singular Sturm-Liouville Boundary Value Problems with Integral Boundary Conditions

In this paper, we study the second-order nonlinear singular Sturm-Liouville boundary value problems with Riemann-Stieltjes integral boundary conditions    −(p(t)u(t)) + q(t)u(t) = f(t, u(t)), 0 < t < 1, α1u(0)− β1u (0) = ∫ 1 0 u(τ)dα(τ), α2u(1) + β2u (1) = ∫ 1 0 u(τ)dβ(τ), where f(t, u) is allowed to be singular at t = 0, 1 and u = 0. Some new results for the existence of positive solu...

Positive Solutions of Sturm-Liouville Boundary Value Problems in Presence of Upper and Lower Solutions

Positive Solutions for Singular Sturm-liouville Boundary Value Problems on the Half Line

This article concerns the existence and multiplicity of positive solutions for the singular Sturm-Liouville boundary value problem (p(t)u′(t))′ + h(t)f(t, u(t)) = 0, 0 < t <∞, au(0)− b lim t→0+ p(t)u′(t) = 0, c lim t→∞ u(t) + d lim t→∞ p(t)u′(t) = 0. We use fixed point index theory to establish our main results based on a priori estimates derived by utilizing spectral properties of associated l...