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Keywords: Positive solutions Third-order three-point BVPs Nonhomogeneous Fixed point theorem Existence and nonexistence a b s t r a c t In this work, by employing the Guo–Krasnosel'skii fixed point theorem and Schauder's fixed point theorem, we study the existence and nonexistence of positive solutions to the third-order three-point nonhomogeneous boundary(More)
In this paper, we consider the second-order three-point boundary-value problem u (t) + f (t, u, u , u) = 0, 0 ≤ t ≤ 1, u(0) = u(1) = αu(η). Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the(More)
We consider classes of second order boundary value problems with a nonlinearity f (t, x) in the equations and subject to a multi-point boundary condition. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. The symmetry of solutions is also studied. Conditions(More)
Recommended by Colin Rogers We study the second-order m-point boundary value problem u (t) + a(t) f (t,u(t)) = 0, 0 < t < 1, u(0) = u(1) = m−2 i=1 α i u(η i), where 0 < η 1 < η 2 < ··· < η m−2 ≤ 1/2, α i > 0 for i = 1,2,...,m − 2 with m−2 i=1 α i < 1,m ≥ 3. a : (0,1) → [0,∞) is continuous, symmetric on the interval (0,1), and maybe singular at t = 0 and t =(More)
Chemical fruit thinning has become a popular practice in modern fruit orchards for achieving high quality fruits, reducing costs of hand thinning and promoting return bloom. However, most of the suggested chemical thinners are often concerned for their detrimental effects and environmental problems. 5-Aminolevulic acid (ALA) is a natural, nontoxic,(More)
In this paper, we study the existence of nontrivial symmetric solution for the second-order three-point boundary value problem for a function f W OE0; 1 R ! R which is continuous and f .t; / is symmetric on OE0; 1. We shall formulate conditions on f which guarantee the existence of nontrivial symmetric solution. As an application, we also give some(More)
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