In this paper, we investigate the existence of concave and monotone positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form. By using a fixed point theorem of cone expansion and compression of norm type, the existence and nonexistence of concave and monotone positive solutions for the above boundary value problems is obtained. Meanwhile, as applications of our results, some examples are given.
MSC: 34B15; 34B18
In this paper, we consider a one-dimensional mean curvature equation in Minkowski space and the corresponding one-parameter problem. By using a fixed point theorem of cone expansion and compression of norm type, the existence and multiplicity of positive solutions for the above problems are obtained. Meanwhile, as applications of our results, some examples are given.
The existence and uniqueness of positive solution is obtained for the singular second-order mpoint boundary value problem u t f t, u t 0 for t ∈ 0, 1 , u 0 0, u 1 m−2 i 1 α i u η i , where m ≥ 3, α i > 0 i 1, 2, . . . , m − 2 , 0 < η 1 < η 2 < · · · < η m−2 < 1 are constants, and f t, u can have singularities for t 0 and/or t 1 and for u 0. The main tool is the perturbation technique and Schauder fixed point theorem.
In the present paper, we prove the existence of at least three radial solutions of the p-Laplacian problem with nonlinear gradient termand the corresponding one-parameter problem. Here is a unit ball in R N . Our approach relies on the Avery-Peterson fixed point theorem. In contrast with the usual hypotheses, no asymptotic behavior is assumed on the nonlinearity f with respect to φ p (·).
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