Chaitan P. Gupta

On an m -point boundary-value problem for second-order ordinary differential equations

where q E (0, 1) is given. We obtain conditions for the existence and uniqueness of a solution for the boundary-value problem (2), using the Leray-Schauder continuation theorem [2]. We give an example of a three-point boundary-value problem where the existence condition is not satisfied and no solution exists. Gupta [3] recently studied the boundary-value problem (2) when Q! = 1. Our results on the three-point boundary-value problem (2) extend the results of Gupta [3], to the case of general CY. (See also [4, 51.) We use the classical spaces C[O, 11, C’[O, 11, Lk[O, 11, and L”[O, l] of continuous, k-times continuously differentiable, measurable real-valued functions whose kth power of the absolute value is Lebesgue integrable on [0, 11, or measurable functions that are essentially bounded

Solvability of a Multi-Point Boundary Value Problem at Resonance

AbstractLet f: [0, 1] × R2 → R be a function satisfying Caratheodory’s conditions and e(t) ∈ L1[0, 1]. Let ηi ∈ (0, 1), i = 1, …, k, with 0 s< η1 < … < ηk < 1, be given. This paper is concerned with the problem of existence of a solution for the multi-point boundary value problem .Conditions for the existence of a solution for the above boundary value problem are given using Leray Schauder Continuation theorem.

L p -solvability of a fourth-order boundary-value problem at resonance

Abstract Let Ω be a bounded domain in R n with smooth boundary Γ. We obtain existence results for the solutions of the biharmonic boundary value problems, -Δ 2 u + ⋋ 2 1 u + g(x, u) = f , in Ω, u = Δu = 0 on Γ; -Δ2u + g(x, u) = f, Ω, ∂u/∂n = ∂(Δu)/∂n = 0 , on Γ when g(x, u) has linear growth in u and f is in certain subclass of L p (Ω) . In the first problem, ⋋1 is the first eigenvalue of the eigenvalue problem -Δu = ⋋u in Ω and u = 0 on Γ.

A sharp conditon for existence of a solution for a fourth order boundary value problem

Let be a function satisfying Caratheodorś conditions and , This paper is concerned with the problem of existence of a solution for the boundary value problem A sharp condition for the existence of a solution of the above boundary value problem is given, using some Wirtinger type inequalites for ([0,1]) with .