Existence of one-signed solutions of nonlinear four-point boundary value problems

In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems $$ - u'' + Mu = rg(t)f(u),u(0) = u(\varepsilon ),u(1) = u(1 - \varepsilon ) $$ and $$u'' + Mu = rg(t)f(u),u(0) = u(\varepsilon ),u(1) = u(1 - \varepsilon ) $$ , where ε ∈ (0, 1/2), M ∈ (0,∞) is a constant and r > 0 is a parameter, g ∈ C([0, 1], (0,+∞)), f ∈ C(?,?) with sf(s) > 0 for s ≠ 0. The proof of the main results is based upon bifurcation techniques.     

Existence and approximation of solutions for nonlinear second-order four-point boundary value problems

Applying the method of upper and lower solutions, Leray–Schauder degree theory and one-sided Nagumo condition, we obtain the existence and uniqueness results for a class of nonlinear second-order four-point boundary value problems. By the generalized approximation method, a monotone iteration sequence which converges uniformly to the unique solution of the nonlinear problem and converges quadratically to the unique solution of the linear problem is also obtained.     

Existence of positive solutions for three-point boundary value problems at resonance

With the help of the theorem of a fixed point index for A-proper semilinear operators established by Cremins, we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three-point boundary value problems at resonance.     

Existence and multiplicity of solutions for fourth-order boundary value problems with parameters

In this paper we study the existence and multiplicity of the solutions for the fourth-order boundary value problem (BVP) u(4)(t)+ηu^″(t)−ζu(t)=λf(t,u(t)), 0<t<1, u(0)=u(1)=u^″(0)=u^″(1)=0, where is continuous, ζ,η∈R and λ∈R⁺ are parameters. By means of the idea of the decomposition of operators shown by Chen [W.Y. Chen, A decomposition problem for operators, Xuebao of Dongbei Renmin University 1 (1957) 95-98], see also [M. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostehizdat, Moscow, 1956], and the critical point theory, we obtain that if the pair (η,ζ) is on the curve ζ=−η²/4 satisfying η<2π², then the above BVP has at least one, two, three, and infinitely many solutions for λ being in different interval, respectively.     

Positive solutions for fractional four-point boundary value problems

In this paper, a fractional four-point boundary value problem is considered. By means of fixed-point theorems and successive iteration method, some results on the existence, multiplicity and uniqueness of positive solutions are obtained.     

Positive solutions for some second-order four-point boundary value problems

In this paper, the second-order four-point boundary value problem

     

共振条件下积分边值问题解的存在性

运用Mawhin重合度理论建立了二阶Stieltjes积分边值问题解的存在性定理,其所得结果推广了多点边值问题已有的一些结论。     

Existence and multiplicity results for nonlinear periodic boundary value problems

This paper studies the existence of positive solutions for periodic boundary value problems. The criteria for the existence, nonexistence and multiplicity of positive solutions are established by using the Global continuation theorem, fixed point index theory and approximate method. The results obtained herein generalize and complement some previous findings of [J.R. Graef, L. Kong, H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differential Equations 245 (2008) 1185–1197] and some other known results.     

Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems

We investigate the existence and multiplicity of positive solutions of multi-point boundary value problems for systems of nonlinear higher-order ordinary differential equations.     

Existence theorems for linear hyperbolic boundary value problems at resonance

Summary Questions of existence, uniqueness, and continuous dependence for weak solutions of linear hyperbolic boundary value problems are considered. The differential equations have the form u_tt + Au=f, where A is elliptic in the spatial variables, and the boundary conditions are homogeneous in both space and time. Resolution of these questions depends on the relationship of the eigenvalues of A and those of an associated scalar problem in time.     

Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance

In this paper, we consider the following two-point boundary value problem for fractional p-Laplace differential equation where $D^{\alpha}_{0^{+}}$ , $D^{\beta}_{0^{+}}$ denote the Caputo fractional derivatives, 0<α,β≤1, 1<α+β≤2. By using the coincidence degree theory, a new result on the existence of solutions for above fractional boundary value problem is obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is inserted to illustrate the validity and practicability of our main results.