[PDF] Top 20 Positive solutions for nonlinear elastic beam models

... appropriate boundary conditions describes various physically important boundary value problems (see [3]). Korman [3] studied the existence of positive solutions of (1.1) by using monotone iterations. His ... See full document

... whose solutions represent the equilibria of a bridge suspended by continuously distributed cables and supported by M intermediate ...extensible elastic beams which are clamped to each other and pinned at ... See full document

... where c = , , , , and . Then, using (), we obtain different positive blow-up solutions of problem (). However, their graphs are again ordered; see Figure . Hence, condition (H   ) seems not to be ... See full document

... study, nonlinear vibrations of an Euler-Bernoulli nanobeam resting on an elastic foundation is studied using nonlocal elasticity ...The nonlinear equation of motion is obtained by including ... See full document

... By using an infinitely many critical points theorem, we study the existence of infinitely many solutions for a fourth-order nonlinear boundary value problem, depending on two real parameters. No symmetric ... See full document

... The subspace we are looking for should satisfy two conditions other than complete- ness: first, it should be invariant under the operator Ψ . Second, the restriction of Ψ to it should be contractive. Once we proved in ... See full document

... where a, b > , F : [, ] × R × R → R is continuous, and the y in F is the bending moment term which represents bending effect. Problem (.) is often referred to as the deformation of an elastic beam ... See full document

... where the nonlinearity −bu crosses an eigenvalue. This equation represents a bending beam supported by cables under a load f. The constant b represents the restoring force if the cables stretch. The nonlinearity u ... See full document

... Fourth-order nonlinear differential equations have many applications such as balancing condition of an elastic beam which may be described by nonlinear fourth-order ordinary differential ...for ... See full document

... theory, beam theory, suffices if only small deflections need to be considered; the majority of structural engineering applications are adequately modelled by a beam; bridges and buildings are not designed to ... See full document

... that beam is one of the basic structures in ...combined beam with rock bolts. The deformations of an elastic beam in equilibrium state, whose two ends are simply supported, can be described by ... See full document

... Problem (5.1) has caused great attention since it generalizes the well-known elastic beam equation [46]. In [47], Goodrich first obtained some properties of the Green’s function cor- responding to (5.1). ... See full document

... Let B : E ® E be a positive completely continuous linear operator, r(B) a spectral radius of B, B* the conjugated operator of B, and P* the conjugated cone of P. Since P ⊂ E is a generating cone, according to the ... See full document

... monotone positive solutions of elastic beam equations with a parameter λ ...the beam is fixed at one end and attached to a bearing device or freed at the other ...the beam ... See full document

... monotone positive solutions for an elastic beam equation with nonlinear boundary conditions, and some sufficient conditions which guarantee the existence of unique monotone ... See full document

... a positive solution of the BVP 1.1 if it satisfies the BVP 1.1 ut > 0, −u t > 0 for t ∈ 0, 1 and u t > 0 for t ∈ 0, 1. For some λ ∈ 0, ∞, if the BVP 1.1 has a positive solution u, then λ is called ... See full document

... We present computations, which suggest efficiency of monotone methods for fourth order boundary value problems... KEY WORDS AND PHRASES..[r] ... See full document

... It follows by the nonnegativity of functions a, b, f, g of parameter λ and a strong maximum principle that all non-negative and nontrivial solutions of 1.1 must be strictly positive see Serrin and Zou 6. ... See full document

... for beam on elastic foundation mainly in mechanical and civil engineering ...on elastic foundations, network of beams in the construction of floor systems for ships, buildings, and bridges, submerged ... See full document

... Fractional differential systems can arise from sciences problems such population problems, dielectric polarization, electromagnetic waves,...see [3]. Many methods are used for the investigation of fractional differential ... See full document