一类具有周期变指数和凹凸非线性项椭圆型方程解的多重性

研究一类具有周期变指数和凹凸非线性项的椭圆边值问题,借Ekeland分原理和Nehari流形等理论和方法得到解的多重性.     

EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS

The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities.It is shown,by means of variational methods,that under certain conditions,the system has at least two positive solutions.     

Existence of multiple positive solutions for semilinear elliptic systems involving m critical hardy-sobolev exponents and m sign-changing weight function

In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.     

Positive solutions for a p−q‐Laplacian system with critical nonlinearities

In this paper, our main purpose is to establish the existence results of positive solutions for a p ?q ‐Laplacian system involving concave‐convex nonlinearities: where Ω is a bounded domain in R ^N , λ ,θ >0 and 1<r <q <p <N . We assume 1<α ,β and is the critical Sobolev exponent and △_s ·=div(|?·|^{s ?2}?·) is the s‐Laplacian operator. The main results are obtained by variational methods.     

Sign-changing solutions for elliptic problems with critical Sobolev-Hardy exponents

Let be a smooth bounded domain such that 0∈Ω, N?7, 0?s<2, 2∗(s)=2(N−s)/(N−2). We prove the existence of sign-changing solutions for the singular critical problem −Δu−μ(u/|x|2)=(|u|2∗(s)−2/|x|s)u+λu with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ.     

On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function

In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign-changing weight function. With the help of the Nehari manifold, we prove that there are at least two positive solutions for Eq. (Eλ,f) in bounded domains.     

Existence of multiple solutions for a fractional p-Laplacian system with concave-convex term

In this article, we study the existence of multiple solutions for the following system driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions{(-?)_p~su = a(x)|u|~(q-2) u +2α/α + βc(x)|u|~(α-2) u|v|~β, in ?,(-?)_p~sv = b(x)|v|~(q-2) v +2β/α + βc(x)|u|α|v|~(β-2) v, in ?,u = v = 0, in Rn\?,(0.1) where Ω is a smooth bounded domain in Rn, n ps with s ∈(0,1) fixed, a(x), b(x), c(x) ≥ 0 and a(x),b(x),c(x) ∈L∞(Ω), 1 q p and α,β 1 satisfy pα + βp*,p* =np/n-ps.By Nehari manifold and fibering maps with proper conditions, we obtain the multiplicity of solutions to problem(0.1).?????     

Existence of positive solutions to fractional elliptic problems with Hardy potential and critical growth

In this work, we study the following critical problem involving the fractional Laplacian: where s ∈ (0,1), N > 2s, , and is the fractional critical exponent, 0 < μ < Λ_N,s, the sharp constant of the Hardy‐Sobolev inequality. For suitable assumptions on g(x) and K(x), we consider the existence and multiplicity of positive solutions depending on the value of p. Moreover, we obtain an existence result for the problem when λ = 0.     

Existence and multiplicity results for critical growth polyharmonic elliptic systems

In the present paper, we deal with the existence and multiplicity of nontrivial solutions for a class of polyharmonic elliptic systems with Sobolev critical exponent in a bounded domain. Some new existence and multiplicity results are obtained. Our proofs are based on the Nehari manifold and Ljusternik–Schnirelmann theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiplicity of nodal solutions for elliptic problems involving non-odd nonlinearities

In this paper, we study the effect of domain shape on the number of 2-nodal solutions for the semilinear elliptic equation involving non-odd nonlinearities. We prove that a semilinear elliptic equation in an m$m$-bump domain (possibly unbounded) has m²$m^2$ 2-nodal solutions and we can find a least energy nodal solution in those solutions. Furthermore, we can describe the bump location of these solutions.     

Existence of solutions of fractional p-Laplacian systems with different critical Sobolev-Hardy exponents

In this paper, we investigate a fractional p-Laplacian system with different critical Sobolev-Hardy exponents. By variational methods and the Mountain-Pass lemma, positive minimizers of the related best Sobolev constants and the existence of positive solutions of the system are found.     

Solutions for quasilinear elliptic problems with critical Sobolev-Hardy exponents

Let N?3, 2<p<N, 0?s<p and . Via the variational methods and analytic technique, we prove the existence of nontrivial solution to the singular quasilinear problem , for N?p² and suitable functions f(u).     

Nehari流形在一个拟线性方程组中的应用

主要研究带有非齐次边界条件的拟线性椭圆方程组的正解问题,在合适参数条件下,用变分方法和流形方法得到该椭圆方程组正解的存在性和多解性.结论推广了近期发表的结果.     

Existence results for degenerate elliptic equations with critical cone Sobolev exponents

In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions.     

Multiplicity of positive solutions for a semilinear p-Laplacian system with Sobolev critical exponent

In this paper, we study the semilinear p-Laplacian system with critical growth terms in bounded domains. By using the Nehari manifold and variational methods, we prove that the system has at least two positive solutions when the pair of the parameters (λ,μ) belongs to a certain subset of R².     

Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents

This paper studies the following nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents where , Ω is a C ¹ open bounded domain in containing the origin, and . The existence result of positive ground state solution is established.