Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem
TL;DR: In this paper, the boundary value problem was considered in the context of boundary value maximization, where the authors considered the problem of finding a boundary value for a given set of variables.
About: This article is published in Journal of Differential Equations.The article was published on 2008-09-01 and is currently open access. It has received 99 citations till now. The article focuses on the topics: Boundary value problem & Multiplicity (mathematics).
Citations
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TL;DR: In this article, the existence of positive solutions for a class of nonlinear boundary value problems with integral boundary conditions was studied, based on the known Guo-Krasnoselskii fixed point theorem.
259 citations
TL;DR: In this article, a type of nonlinear fractional boundary value problem with non-homogeneous integral boundary conditions is studied, and the existence and uniqueness of positive solutions are discussed.
Abstract: The authors study a type of nonlinear fractional boundary value problem with non-homogeneous integral boundary conditions. The existence and uniqueness of positive solutions are discussed. An example is given as the application of the results.
66 citations
TL;DR: In this article, a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results, is presented, based on the local existence of positive solutions for nonlinear boundary value problems.
47 citations
TL;DR: In this paper, a class of second order impulsive differential equations with integral boundary conditions is studied and various existence, multiplicity, and nonexistence results for positive solutions are derived in terms of the parameter lies in some intervals.
40 citations
Additional excerpts
...Some ideas of this paper are from [17,18]....
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TL;DR: The existence, multiplicity, and nonexistence results of nontrivial solutions are obtained for discrete nonlinear fourth-order boundary value problems with three parameters based on the critical point theory and monotone operator theory.
36 citations
References
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Book•
01 Jan 1941
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Abstract: Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Second-order elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques Hamilton-Jacobi equations Systems of conservation laws Appendices Bibliography Index.
25,734 citations
Book•
01 Jan 1964
2,084 citations
Additional excerpts
...Lemma 3.2. (See [4, 6 ].) Let X be a Banach space and let K ⊂ X be a cone in X. Assume Ω1 ,Ω 2 are bounded open subsets of X with 0 ∈ Ω1 ⊂ Ω 1 ⊂ Ω2 and let...
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TL;DR: In this article, the existence of periodic solutions of the second-order Caratheodory problem is studied, by combining some new properties of Green's function together with Krasnoselskii fixed point theorem on compression and expansion of cones.
290 citations
"Existence, multiplicity, and depend..." refers background in this paper
...[5], Li [7], O’Regan and Wang [10], Torres [11], and Zhang and Wang [13]....
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...All rights reserved. doi:10.1016/j.jde.2008.06.012 examples, we mention the papers of Atici and Guseinov [3], Jiang et al. [5], Li [7], O’Regan and Wang [10], Torres [11], and Zhang and Wang [13]....
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TL;DR: In this article, the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system ( Φ ( u ′ ))′+λ h (t) f(u) = 0, 0 Φ is shown.
184 citations