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1.
In this paper, by using fixed point theorems in cones, some new existence criteria for positive solutions of the nonlinear m-point boundary value problem with an increasing homeomorphism and positive homomorphism are presented. The nonlinear term f is allowed to change sign. In particular, our criteria generalize and improve some known results [20] and the obtained conditions are different from related literature [16], [17], [23]. As an application, one representative example to demonstrate our results are given.  相似文献   

2.
In this paper, we consider the existence of positive solutions for a high-order semipositone fractional differential equation with Riemann-Stieltjes integral boundary conditions. By Krasnoselskii-Zabreiko fixed point theorem and some inequalities associated with Green’s function, two new existence theorems are obtained in the case that the nonlinearity f is allowed to grow both superlinearly and sublinearly. Finally, two examples are given to illustrate the main results.  相似文献   

3.
The existence of solutions of the following multi-point boundary value problem $\left\{ \begin{gathered} x^{(n)} (t) = f(t,x(t),x^\prime (t),...,x^{(n - 2)} (t)) + r(t),0 < t < 1, \\ x^{(i)} (\xi _i ) = 0 for i = 0,1,... ,n - 3, ( * ) \\ \alpha x^{(n - 2)} (0) = \beta x^{(n - 1)} (0) = \gamma x^{(n - 1)} (1) + \tau x^{(n - 1)} (1) = 0 \\ \end{gathered} \right.$ is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don’t apply the Green’s functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.  相似文献   

4.
By means of Mawhin’s continuation theorem, a second order differential equation with a deviating argument is studied. A new result on the existence of periodic solutions is obtained. Meanwhile, the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature.  相似文献   

5.
In this paper, we consider the existence of multiple positive solutions for the following singular semipositone Dirichlet boundary value problem: $$\left\{\begin{array}{l}-x''(t)=p(t)f(t, x) +q(t),\quad t\in(0,1),\\[4pt]x(0) =0,\qquad x(1) = 0,\end{array}\right.$$ where p:(0,1)??[0,+??) and f:[0,1]×[0,+??)??[0,+??) are continuous, q:(0,1)??(???,+??) is Lebesgue integrable. Under certain local conditions and superlinear or sublinear conditions on f, by using the fixed point theorem, some sufficient conditions for the existence of multiple positive solutions are established for the case in which the nonlinearity is allowed to be sign-changing.  相似文献   

6.
Considered is the periodic functional differential system with a parameter, x(t)=A(t,x(t))x(t)+λf(t,xt). Using the eigenvalue problems of completely continuous operators, we establish some criteria on the existence of positive periodic solutions. Moreover, we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions, which are compared with existing ones.  相似文献   

7.
In this paper, we study the existence and multiplicity of solutions of the operator equation Kfu=u in the real Hilbert space L2(G). Under certain conditions on the linear operator K, we establish the conditions on f which are able to guarantee that the operator equation has at least one solution, a unique solution, and infinitely many solutions, respectively. The monotone operator principle and the critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator K1/2 and its properties play an important role. As an application, we investigate the existence and multiplicity of solutions to fourth-order boundary value problems for ordinary differential equations with two parameters, and give some new existence results of solutions.  相似文献   

8.
In this paper, we study the existence of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions and a parameter. By using the properties of the Green’s function, u 0-positive function and the fixed point index theory, we obtain some existence results of positive solution under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The method of this paper is a unified method for establishing the existence of multiple positive solutions for a large number of nonlinear differential equations of arbitrary order with any allowed number of non-local boundary conditions.  相似文献   

9.
In this paper we consider a reaction-diffusion-chemotaxis aggregation model of Keller-Segel type with a nonlinear, degenerate diffusion. Assuming that the diffusion function f(n) takes values sufficiently large, i.e. takes values greater than the values of a power function with sufficiently high power (f(n)?δnp for all n>0, where δ>0 is a constant), we prove global-in-time existence of weak solutions. Since one of the main features of Keller-Segel type models is the possibility of blow-up of solutions in finite time, we will derive the uniform-in-time boundedness, which prevents the explosion of solutions. The uniqueness of solutions is proved provided that some higher regularity condition on solutions is known a priori. Finally, computational simulation results showing the effect of three different types of diffusion function are presented.  相似文献   

10.
We study local analytic solutions f of the generalized Dhombres functional equation f(zf(z))=φ(f(z)), where φ is holomorphic at w0≠0, f is holomorphic in some open neighborhood of 0, depending on f, and f(0)=w0. After deriving necessary conditions on φ for the existence of nonconstant solutions f with f(0)=w0 we describe, assuming these conditions, the structure of the set of all formal solutions, provided that w0 is not a root of 1. If |w0|≠1 or if w0 is a Siegel number we show that all formal solutions yield local analytic ones. For w0 with 0<|w0|<1 we give representations of these solutions involving infinite products.  相似文献   

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