Existence of positive solutions for boundary value problems of second-order functional-differential equations.
Singular positone and semipositone boundary value problems of nonlinear fractional differential equations.
Positive periodic solutions of functional differential equations and population models.
Existence and uniqueness of solutions for boundary value problems to the singular one-dimension -Laplacian.
Existence and uniqueness of solutions for singular higher order continuous and discrete boundary value problems.
Multiple positive solutions to singular boundary value problems for superlinear second order FDEs
We study the existence of positive solutions to the singular boundary value problem for a second-order FDE ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1, ⎨ u(t) = ξ(t), a ≤ t ≤ 0, ⎩ u(t) = η(t), 1 ≤ t ≤ b, where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
On second order periodic boundary-value problems with upper and lower solutions in the reversed order.
Upper and lower solutions for a second-order three-point singular boundary-value problem.
A note on periodic solutions of second order nonautonomous singular coupled systems.
Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation.
Existence theory for single and multiple solutions to semipositone discrete Dirichlet boundary value problems with singular dependent nonlinearities.
On the existence of nonnegative radial solutions for p-Laplacian elliptic systems
The existence of nonnegative radial solutions for some systems of m (m ≥ 1) quasilinear elliptic equations is proved by a simple application of a fixed point theorem in cones.
Multiple positive solutions of a nonlinear fourth order periodic boundary value problem
The fourth order periodic boundary value problem , 0 < t < 2π, with , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of .
A generalized periodic boundary value problem for the one-dimensional p-Laplacian
The generalized periodic boundary value problem -[g(u’)]’ = f(t,u,u’), a < t < b, with u(a) = ξu(b) + c and u’(b) = ηu’(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, , p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.
A monotone method for constructing extremal solutions to second order periodic boundary value problems
We describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) in the presence of a lower solution α(t) and an upper solution β(t) with β(t) ≤ α(t).
Population dynamical behavior of a single-species nonlinear diffusion system with random perturbation
We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation.
Multiplicity of positive solutions to second order differential equations with Neumann boundary conditions
We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.
Existence theory for single and multiple solutions to singular positone boundary value problems for the delay one-dimensional p-Laplacian
The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.
Singular positone and semipositone boundary value problems of second order delay differential equations
In this paper we present some new existence results for singular positone and semipositone boundary value problems of second order delay differential equations. Throughout our nonlinearity may be singular in its dependent variable.
Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension -Laplacian
In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem where , and our nonlinear term may be singular at .
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