143 research outputs found
Existence of solutions for quasilinear elliptic equations with Hardy potential
No full textIn this paper, we consider the following quasilinear elliptic equation with Hardy potential and Dirichlet boundary condition: -Sigma(N)(i,j=1) D-j(a(i j)(x, u)D(i)u) + 1/2 Sigma(N)(i,j=1) D(s)a(i,j)(x, u)D(i)uD(j)u - lambda|x|(-2)u = f (x, u) in Omega, where Omega subset of R-N (N >= 3) is a smooth bounded domain, D-i = partial derivative/partial derivative x(i), D(s)a(i j)(x, s) = partial derivative/partial derivative s a(i j)(x, s), and 0 <= lambda < lambda* := (N-2/2)(2), and lambda|x|(-2) is called the Hardy potential. By using the perturbation method, we prove the existence of infinitely many solutions for the above problem. (C) 2016 AIP Publishing LLC.NSFC [11151040, 11331010, 11371160, 11271331]SCI(E)[email protected]; [email protected]; [email protected]
THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS IN Rn FOR SEMILINEAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT
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Multiplicity of stationary solutions to the Euler–Poisson equations
No full textAbstractConsider the system of Euler–Poisson as a model for the time evolution of gaseous stars through the self-induced gravitational force. We study the existence, uniqueness and multiplicity of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy a priori. These results generalize the previous works on the irrotational or the rotational gaseous stars around an axis, and then they hold in more general physical settings. Under the assumption of radial symmetry, the monotonicity properties of the radius of the gas with respect to either the strength of the velocity field or the center density are also given which yield the uniqueness under some circumstances
On the Existence of Multiple Positive Solutions for a Semilinear Problem In Exterior Domains
Get PDFIn this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=N\ω is an exterior domain in N, ω⊂N is a bounded domain with smooth boundary, and N\u3e2. μ⩾0, p\u3e1 are some given constants. K(x) satisfies: K(x)∈Cαloc(Ω) and ∃C, ϵ, M\u3e0 such that |K(x)|⩽C |x|l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and nonexistence of multiple solutions have been discussed under different assumptions on K
Regularity of the Solutions for Nonlinear Biharmonic Equations in Rn
No full textThe purpose of this paper is to establish the regularity the weak solutions for a nonlinear biharmonic equation
ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS
No full textOn inhomogeneous biharmonic equations involving critical exponents
No full textIn this paper, we consider the existence of multiple solutions of biharmonic equations boundary value problemwhere Ω is a bounded smooth domain in ℝN, N ≥ 5; λ ∈ ℝ1 is a given constant; p = 2N/(N − 4) is the critical Sobolev exponent for the embedding ; Δ2 = ΔΔ denotes iterated N-dimensional Laplacian; f(x) is a given function. Some results on the existence and non-existence of multiple solutions for the above problem have been obtained by Ekeland's variational principle and the mountain-pass lemma under some assumptions on f(x) and N.</jats:p
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