Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Existence and Concentration of Sign-Changing Solutions of Quasilinear Choquard Equation

In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on RN × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, Iα is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .

SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

In this paper, we study the existence of least energy sign-changing solutions for aKirchhoff-type problem involving the fractional Laplacian operator. By using the constraintvariation method and quantitative deformation lemma, we obtain a least energy nodal solu-tion ub for the given problem. Moreover, we show that the energy of ub is strictly larger thantwice the ground state energy. We also give a convergence property of ub as b O, where bis regarded as a positive parameter.

INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL

In this article, we give a new proof on the existence of infinitely many sign- changing solutions for the following Brezis-Nirenberg problem with critical exponent and a Hardy potential -△u-μ（u/｜x｜^2）=λu＋｜u｜^2＊-2u inΩ, u=0 on eΩ,where Ω is a smooth open bounded domain of R^N which contains the origin, 2＊=2N/n-2 is the critical Sobolev exponent. More precisely, under the assumptions that N ≥ 7, μ ∈ [0, μ- 4）, and μ=（N-2）^2/4, we show that the problem admits infinitely many sign-changing solutions for each fixed λ 〉 0. Our proof is based on a combination of invariant sets method and Lj usternik-Schnirelman theory.

SIGN-CHANGING SOLUTIONS FOR p-BIHARMONIC EQUATIONS WITH HARDY POTENTIAL IN R^N

In this article, by using the method of invariant sets of descending flow, we obtain the existence of sign-changing solutions of p-biharmonic equations with Hardy potential in RN.

SIGN-CHANGING SOLUTIONS FOR SCHRDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

In this article, we study the existence of sign-changing solutions for the following SchrSdinger equation -△u ＋ λV（x）u = K（x）｜u｜^p-2u x∈R^N, u→0 as ｜x｜→ ＋∞, 2N where N ≥ 3, λ〉 0 is a parameter, 2 〈 p 〈 2N/N-2, and the potentials V（x） and K（x） satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011].

Existence of Sign-changing Solution for Three-point Boundary Value Problems

In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.

Sign-Changing Solutions for Discrete Dirichlet Boundary Value Problem

Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.

A SIGN CHANGING SOLUTION FOR ELLIPTIC EQUATION WITH SUBLINEAR TERM AT ORIGIN

It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).

Study on the Existence of Sign-Changing Solutions of Case Theory Based a Class of Differential Equations Boundary-Value Problems

By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.

Sign Changing Solution of a Semilinear Schrödinger Equation with Constraint

The purpose of this paper is to study a semilinear Schrödinger equation with constraint in H1(RN), and prove the existence of sign changing solution. Under suitable conditions, we obtain a negative solution, a positive solution and a sign changing solution by using variational methods.

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRDINGER-POISSON EQUATIONS WITH SIGN-CHANGING POTENTIAL

In this article, we study the following nonhomogeneous Schrodinger-Poissone quations{-△u＋λV（x）u＋K（x）Фu=f（x,u）＋g（x）,x∈R^3,-△Ф=k（x）u^2, x∈R^3}where λ 〉 0 is a parameter. Under some suitable assumptions on 11, K, f and g, the existence of multiple solutions is proved by using the Ekeland＇s variational principle and the Mountain Pass Theorem in critical point theory. In particular, the potential V is allowed to be signchanging.

Existence of Sign-Changing Solution with Least Energy for a Class of Schrödinger-Poisson Equations in R³

The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schrödinger-Poisson equation. We consider a class of Schrödinger-Poisson equation with variable potential under weaker conditions in this paper. By introducing some new techniques and using truncated functional, Hardy inequality and Pohožaev identity, we obtain an existence result of a least energy sign-changing solution and a ground state solution for this kind of Schrödinger-Poisson equation. Moreover, the energy of the sign-changing solution is strictly greater than the ground state energy.

Multiple Solutions to the Problem of Kirchhoff Type Involving the Critical Caffareli-Kohn-Niremberg Exponent, Concave Term and Sign-Changing Weights

In this paper, we establish the existence of at least four distinct solutions to an Kirchhoff type problems involving the critical Caffareli-Kohn-Niremberg exponent, concave term and sign-changing weights, by using the Nehari manifold and mountain pass theorem.

Multiple Solutions for an Elliptic Equation with Hardy-Sobolev Critical Exponent, Hardy-Sobolev-Maz’ya Potential and Sign-Changing Weights

In the present paper, an elliptic equation with Hardy-Sobolev critical exponent, Hardy-Sobolev-Maz’ya potential and sign-changing weights, is considered. By using the Nehari manifold and mountain pass theorem, the existence of at least four distinct solutions is obtained.

BOUND STATES FOR A STATIONARY NONLINEAR SCHRDINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3

We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0

THE POSITIVE SOLUTION OF CLASSICAL GELFAND MODEL WITH COEFFICIENT THAT CHANGE SIGN

The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.

“基于海洋解决方案倡议”在应对气候变化领域的应用思考

海洋在减缓和适应全球气候变化中发挥着重要作用,“基于海洋解决方案倡议”,旨在通过采取海洋相关的措施来应对气候变化和减少气候变化对海洋生态系统及其服务功能产生的影响。国内外对于海洋在应对气候变化方面的作用开展了大量研究和实践,结果证明海洋可再生能源利用、海洋生态保护修复和海洋保护地建设等均可有效缓解气候变化造成的负面影响。基于海洋解决方案可进一步用于国家减缓和适应气候变化,考虑纳入国家履行自主贡献目标之一,并通过进一步强化基于海洋解决方案的相关技术研究,建立跨部门协调机制,积极开展国际合作,推动基于海洋解决方案应用本土化和主流化。

一种冻土温度场方程的解析解

冻土在我国分布十分广泛,冻胀现象是冻土区经常出现的问题,其导致的工程病害屡见不鲜。冻胀主要是由土体内部温度变化及水分迁移造成的,是一类极其复杂的温度、渗流及应力多场耦合问题。通过对冻土中的温度场进行分析,求解含冰量及孔隙率随温度变化条件下的冻土一般性瞬态热传导方程,获得其近似解析解并应用于冻土热传导过程的预测。通过与有限元计算所得精确解对比,验证其有效性。研究成果对冻土冻胀问题的深入研究具有一定的理论和实践意义。