Existence theorems for a second order nonlinear differential equation with nonlocal boundary conditions and their applications

2009 ◽  
Vol 33 (1-2) ◽  
pp. 137-153 ◽  
Author(s):  
Meiqiang Feng ◽  
Xuemei Zhang ◽  
Weigao Ge
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Existence Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order ◽  
Order Nonlinear Differential Equation

scholarly journals ON NONLINEAR SPECTRA FOR SOME NONLOCAL BOUNDARY VALUE PROBLEMS

2008 ◽  
Vol 13 (1) ◽  
pp. 87-97 ◽  
Author(s):  
N. Sergejeva
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Second Order ◽  
Nonlocal Boundary Value Problems ◽  
Order Nonlinear Differential Equation ◽  
Nonlocal Integral Condition

We consider a second order nonlinear differential equation with nonlocal (integral) condition. The spectrum of it differs essentially from the known ones.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

scholarly journals General boundedness theorems to some second order nonlinear differential equation with integrable forcing term

1995 ◽  
Vol 18 (4) ◽  
pp. 823-824 ◽  
Author(s):  
Allan Kroopnick
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Real Line ◽  
Integrable Function ◽  
Second Order ◽  
Boundedness Theorem ◽  
Forcing Term ◽  
Order Nonlinear Differential Equation

In this note we present a boundedness theorem to the equationx″+c(t,x,x′)+a(t)b(x)=e(t)wheree(t)is a continuous absolutely integrable function over the nonnegative real line. We then extend the result to the equationx″+c(t,x,x′)+a(t,x)=e(t). The first theorem provides the motivation for the second theorem. Also, an example illustrating the theory is then given.

Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems

1999 ◽  
Vol 6 (5) ◽  
pp. 415-420
Author(s):  
John M. Davis ◽  
Paul W. Eloe ◽  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Three Solutions ◽  
Continuous Growth ◽  
Order Nonlinear Differential Equation ◽  
Triple Positive Solutions

Abstract For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.

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