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This article considers elliptic problems of Kirchhoff-type. We give some new definitions of lower and upper solutions for the problem and establish the method of lower and upper solutions when the upper and lower solutions are well ordered, i.e., the lower solution is less than the upper one, and we also consider the case when the upper and lower solutions have opposite ordering. In addition we use the relation between the topological degree and strict upper and lower solutions in both cases and using this we obtain multiplicity results for nonlinear Kirchhoff-type elliptic problems. [ABSTRACT FROM AUTHOR]

In this article, using the sub-supersolution method and Rabinowitz- type global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems. [ABSTRACT FROM AUTHOR]

In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundary value problems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign. [ABSTRACT FROM AUTHOR]

In this paper, using the theory of fixed point index on a cone and the Leray-Schauder fixed point theorem, we present the multiplicity of positive solutions for the singular nonlocal boundary-value problems involving nonlinear integral conditions and the existence of at least one positive solution for the singular nonlocal boundary-value problems with sign-changed nonlinearities. [ABSTRACT FROM AUTHOR]