Author
Tianlan Chen
Bio: Tianlan Chen is an academic researcher from Northwest Normal University. The author has contributed to research in topics: Neumann boundary condition & Boundary value problem. The author has an hindex of 4, co-authored 6 publications receiving 41 citations.
Papers
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TL;DR: In this article, the existence of positive ω -periodic solutions for the equation u ∈ C ( R, [ 0, ∞ ) ) was studied. The proofs of the main results were based upon fixed point index theory.
14 citations
TL;DR: In this paper, the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, where is continuous, is proved based on the Krein-Rutman theorem and the global bifurcation technique.
Abstract: We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, , , , , , , where is continuous, are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques.
11 citations
TL;DR: In this paper, the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions was proved by combining some properties of Green's function with the fixed-point theorem in cones.
Abstract: We prove the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions by combining some properties of Green's function with the fixed-point theorem in cones.
8 citations
TL;DR: In this paper, the existence of nonnegative, nonconstant and non-decreasing solutions of radial positive solutions of elliptic systems of the form====== −Δu+u=f(u,v)in BR,−Δv+v=g(u and v)inBR, ∂νu=∂νv=0on∂BR,====== where f and g are nondecreasing in each component
7 citations
TL;DR: In this paper, the quadrature method was used to find positive solutions for the semipositone Neumann problems when the parameter λ belongs to some intervals, where λ is defined as a function of the sign of λ.
Abstract: In this paper, by using the quadrature method, we show how changes in the sign of f lead to multiple positive solutions for the semipositone Neumann problems $$-u''(x)=\lambda f\bigl(u(x)\bigr),\qquad u'(0)=0=u'(1), $$
when the parameter λ belongs to some intervals.
3 citations
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Book•
[...]
01 Jan 1982
TL;DR: Theorem of Borsuk and Topological Transversality as mentioned in this paper, the Lefschetz-Hopf Theory, and fixed point index are the fundamental fixed point theorem.
Abstract: Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index
688 citations
TL;DR: In this paper, the authors prove the existence of renormalized solutions to general nonlinear elliptic equation in Musielak-Orlicz space avoiding growth restrictions without any particular type of growth condition of M or its conjugate M ⁎.
58 citations
TL;DR: In this article, the existence of at least one positive solution of the problem is investigated, and the authors show that this problem admits at least a positive solution. And they give a specific example illustrating these generalizations and improvements.
Abstract: We consider the existence of at least one positive solution of the problem $${-y''(t)=f(t,y(t)), y(0)=H_1(\varphi(y))+\int_{E}H_2(s,y(s))\,ds, y(1)=0}$$
, where $${y(0)=H_1(\varphi(y))+\int_{E}H_2(s,y(s))\,ds}$$
represents a nonlinear, nonlocal boundary condition. We show by imposing some relatively mild structural conditions on f, H
1, H
2, and $${\varphi}$$
that this problem admits at least one positive solution. Finally, our results generalize and improve existing results, and we give a specific example illustrating these generalizations and improvements.
23 citations
TL;DR: In this article, the authors considered the problem of finding a radial solution for 1 p ∞, where p = 2 and, with the (k + 1)-th radial eigenvalue of the Neumann Laplacian, there exists a solution having exactly k intersections with u ≡ 1, for a large class of nonlinearities.
Abstract: For 1 p ∞ , we consider the following problem − Δ p u = f ( u ), u > 0 in Ω , ∂ ν u = 0 on ∂Ω , where Ω ⊂ ℝ N is either a ball or an annulus. The nonlinearity f is possibly supercritical in the sense of Sobolev embeddings; in particular our assumptions allow to include the prototype nonlinearity f ( s ) = − s p −1 + s q −1 for every q > p . We use the shooting method to get existence and multiplicity of non-constant radial solutions. With the same technique, we also detect the oscillatory behavior of the solutions around the constant solution u ≡ 1. In particular, we prove a conjecture proposed in [D. Bonheure, B. Noris and T. Weth, Ann. Inst. Henri Poincare Anal. Non Lineaire 29 (2012) 573−588], that is to say, if p = 2 and , with the ( k + 1)-th radial eigenvalue of the Neumann Laplacian, there exists a radial solution of the problem having exactly k intersections with u ≡ 1, for a large class of nonlinearities.
19 citations
TL;DR: The main results are illustrated with several examples and the existence of positive ω -periodic solutions for the delay differential equations is investigated.
19 citations