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

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

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...

Three Positive Solutions of Sturm–liouville Boundary Value Problems for Fractional Differential Equations

We establish the results on the existence of three positive solutions to Sturm-Liouville boundary value problems of the singular fractional differential equation with the nonlinearity depending on D 0+u ⎪⎨ ⎪⎩ D0+u(t)+ f (t,u(t),D μ 0+ u(t)) = 0, t ∈ (0,1),1 < α < 2, a limt→0 I2−α 0+ u(t)−b limt→0 [ I2−α 0+ u(t) ]′ = ∫ 1 0 g(s,u(s),D μ 0+u(s))ds, c D 0+u(1)+du(1) = ∫ 1 0 h(s,u(s),D μ 0+u(s))ds. ...