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In this paper, we study the multiplicity of non‐negative solutions for the quasilinear p‐Laplacian equation with the nonlinear boundary condition (1) where Δp denotes the p‐Laplacian operator, defined by △ pu = div( | ? u | p ? 2 ? u),1 < p < N, Ω is a smooth exterior domain in . is the outward normal derivative, . The parameters p,q,r are either or . The weight functions a(x),h(x),g(x) satisfy some suitable conditions. Using the decomposition of the Nehari manifold and the variational methods, we prove that problem (1) has at least two positive solutions provided 0 < | λ | < λ1 for some λ1. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

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In this paper, we study the existence of a positive ground state solution to the following coupled system of nonlinear Schrödinger equations: where the nonlinearities f1(x,s) and f2(x,s) are superlinear at infinity and have exponential critical growth of the Trudinger‐Moser type. The potentials V1(x) and V2(x) are nonnegative and satisfy a condition involving the coupling term λ(x), namely, λ(x)2<δ2V1(x)V2(x) for some 0<δ<1. For this purpose, we use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap argument and Lq‐estimates, we get regularity and asymptotic behavior.  相似文献   

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In this paper, we prove the existence of ground state sign‐changing solutions for the following class of elliptic equation: where , and K(x) are positive continuous functions. Firstly, we obtain one ground state sign‐changing solution ub by using some new analytical skills and non‐Nehari manifold method. Furthermore, the energy of ub is strictly larger than twice that of the ground state solutions of Nehari type. We also establish the convergence property of ub as the parameter b↘0. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

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Let BR be the ball centered at the origin with radius R in RN ( N ≥2). In this paper we study the existence of solution for the following elliptic systemu -△u+λu=p/(p + q)κ(| x |)) u(p-1)vq1,x ∈BR1,-△u+λu=p/(p + q)κ(| x |)) upv(q-1)1,x ∈BR1,u > 01,v > 01,x ∈ BR1,(u)/(v)=01,(v)/(v)=01,x ∈BRwhereλ > 0 , μ > 0 p ≥ 2, q ≥ 2,ν is the unit outward normal at the boundary BR . Under certainassumptions on κ ( | x | ), using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity.  相似文献   

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In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (Eλ,μ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of R2.  相似文献   

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We study the Schrödinger-KdV system{Δu+λ1(x)u=u3+βuv,uH1(N),Δv+λ2(x)v=12v2+β2u2,vH1(N),where N=1,2,3, λi(x)C(N,),lim|x|λi(x)=λi(), and λi(x)λi(),i= 1,2,a.e. xN.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.  相似文献   

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In this paper, we are concerned with a class of fractional Schrödinger-Poisson system involving subcritical or critical nonlinearities. By using the Nehari manifold and variational methods, we obtain the existence and multiplicity of nontrivial solutions.  相似文献   

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研究了一类含Sobolev临界指数的p-Laplacian奇异拟线性椭圆方程组,利用变分方法,结合Nehari流形和集中紧性原理证明对应的能量泛函满足局部(PS)条件,得到了这一方程组正基态解的存在性.  相似文献   

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