Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities

In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation $$ \left\{ - \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3, \right. $$ where $1相似文献   

辽代绿琉璃瓦残块的分析研究

琉璃瓦作为古代高等级的建筑材料,从北魏时期就在宫殿、皇家寺庙上开始应用,辽宋时期除了应用在皇室建筑上,并且开始在陵园建筑上使用琉璃瓦。现存的明清时期琉璃瓦普遍存在釉层大量脱落的状况,但研究的这件辽代的绿琉璃瓦残块上,虽然釉层极薄、冰裂纹遍布、表面发白,釉层却整体保存十分完好,几乎没有明显起翘脱落,且具有很好的强度。采用超景深显微观察、扫描电镜能谱分析和X射线衍射分析,结合文献资料,对辽宁北镇医巫闾山辽代帝陵遗址中的新立遗址出土绿琉璃瓦残块进行胎、釉的成分分析,研究其烧造工艺,并对其保存现状和釉层保存完好的原因进行深入探讨。结果表明该绿琉璃瓦胎体原料为优质瓷土加上少量小颗粒砂石,其晶相有石英、α-方石英、硅线石、刚玉,是瓷土作胎的较早范例,为我国使用瓷土烧制琉璃瓦的早期历史和工艺发展提供了佐证。绿色釉层属于PbO-SiO₂-Al₂O₃基础釉体系,以Cu为呈色元素,Pb含量低于明清琉璃瓦,其成分中ZnO的缺失可能是釉面青绿色深浅不一、光泽度较低的原因。绿釉几乎无剥离,胎釉结合强度很好,是由于低铅薄釉降低了热膨胀系数、缓解了应力,胎釉热膨胀系数相配,表层浅裂缝不易联通内部与外界环境。加之其使用和保存环境都较为干燥,降低了水的影响,几乎没出现吸湿膨胀和冰冻膨胀。该工作可为相似文物样品的研究、辽代建筑琉璃构件工艺的研究和琉璃文物的病害和保存提供参考。     

ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n = p

This article deals with the problem where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.     

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRDINGER-POISSON EQUATIONS WITH SIGN-CHANGING POTENTIAL

In this article, we study the following nonhomogeneous Schr¨odinger-Poisson equations -?u + λV(x)u + K(x)φu = f(x, u) + g(x), x ∈ R~3,?-?φ = K(x)u~2, x ∈ R~3,where λ 0 is a parameter. Under some suitable assumptions on V, 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 infinitely many homoclinic orbits in discrete Hamiltonian systems

By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order self-adjoint discrete Hamiltonian system Δ[p(n)Δu(n−1)]−L(n)u(n)+∇W(n,u(n))=0 has infinitely many homoclinic orbits, where n∈Z, u∈RN, p,L:Z→RN×N and W:Z×RN→R are no periodic in n. Our conditions on the potential W(n,x) are rather relaxed.     

Bounded Palais-Smale sequences for non-differentiable functions

The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma.     

Boundary value problems of second order nonlinear functional difference equations

By using the critical point theory, some sufficient conditions for the existence and multiplicity of the boundary value problems to a class of second order functional difference equations are obtained.     

Existence and multiplicity results for the nonlinear Schrödinger-Poisson systems

In this paper, we study the existence and multiplicity results for the nonlinear Schrödinger-Poisson systems

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