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We consider linear and nonlinear boundary value problems for third-order difference equations with three-point right focal boundary conditions. In the linear case, the existence of positive solutions corresponding to the first eigenvalue of the problem is established and an interval estimate for the first eigenvalue is obtained. In the nonlinear case, sufficient conditions for the existence and nonexistence of positive solutions are obtained. An example is included at the end of the paper to illustrate the sharpness of our results. 相似文献
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Stephen Clark Johnny Henderson 《Proceedings of the American Mathematical Society》2006,134(11):3363-3372
For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -point boundary conditions. These relationships are investigated as well.
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Under certain conditions, solutions of the boundary value problem, y″=f(x,y,y′), y(x1)=y1, and , are differentiated with respect to boundary conditions, where a<x1<η1<?<ηm<x2<b, r1,…,rm∈R, and y1,y2∈R. 相似文献
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The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of
the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a
comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity
f are related to its behavior only in a neighbourhood of zero and/or of infinity. 相似文献
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Steve Tefteller 《Annali di Matematica Pura ed Applicata》1973,96(1):185-192
Summary This work is concerned with the behavior of solutions of third order self-adjoint differential equations. It is well known
that products of solutions of a second order self-adjoint equation are solutions of the third order equation. A converse of
this fact is established. Existence of oscillatory solutions and asymptotic behavior of nonoscillatory solutions is established.
Separation and comparison theorems are obtained for such equations.
Entrata in Redazione il 13 aprile 1972. 相似文献
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Existence of solutions of boundary value problems for second order functional differential equations
In this paper, we deal with the boundary value problem
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In this paper, we deal with the mixed initial boundary value problem for complete second order (in time) linear differential equations in Banach spaces, in which time-derivatives occur in the boundary conditions. General wellposedness theorems are obtained (for the first time), which are used to solve the corresponding inhomogeneous problems. Examples of applications to initial boundary value problems for partial differential equations are also presented. 相似文献
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Existence and uniqueness results for three-point boundary value problems for the third order nonlinear differential equations are obtained. The results are better than those obtained recently by Barr and Sherman, using extra conditions. 相似文献
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We obtain sufficient conditions for the existence of periodic solutions of the following third order nonlinear functional differential equations
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This paper is devoted to study the existence of multiple positive solutions for the second order Dirichlet boundary value problem with impulse effects. The main results here is the generalization of Liu and Li [L. Liu, F.Y. Li, Multiple positive solution of nonlinear two-point boundary value problems, J. Math. Anal. Appl. 203 (1996) 610-625] for ordinary differential equations. Existence is established via the theory of fixed point index in cones. 相似文献