Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach

Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach

We investigate the existence of positive or a negative solution of several classes of fourpoint boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a positive Green’s function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the cont...

Fourth-order four-point boundary value problem on time scales

and Applied Analysis 3 Using the initial conditions 2.3 , we can deduce from 2.2 for φ and ψ the following equations: φ t η ζ t − ξ1 ∫ t ξ1 ∫ τ ξ1 q s φ σ s ΔsΔτ, 2.5

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...

Existence of Solutions for Fourth-Order Four-Point Boundary Value Problem on Time Scales

Multiple Positive Solutions to a Fourth-order Boundary-value Problem

We study the existence, localization and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnosel’skĭı’s compression-expansion theorem, and unilateral Harnack type inequalities.