共查询到20条相似文献,搜索用时 0 毫秒
1.
We study nonlinear eigenvalue problems for the p-Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik–Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and isolation of the principal eigenvalue and give a characterization for the second eigenvalue. 相似文献
2.
In this paper we establish a priori bounds for positive solutions of the equation
3.
We study the existence and nonexistence of positive (super)solutions to the nonlinear p-Laplace equation
4.
In this paper, we construct the pseudo-gradient vector field in , by which we obtain the positive and negative cones of are both invariant sets of the descent flow of the corresponding functional. Then we use differential equations theory in Banach spaces and dynamics theory to study p-Laplacian boundary value problems with “jumping” nonlinearities at zero or infinity, and get new multiple solutions and sign-changing solutions theorems of p-Laplacian. 相似文献
5.
In this paper we consider a nonlinear eigenvalue problem driven by the p-Laplacian differential operator and with a nonsmooth potential. Using degree theoretic arguments based on the degree map for certain operators of monotone type, we show that the problem has at least two nontrivial positive solutions as the parameter λ>0 varies in a half-line. 相似文献
6.
András Domokos 《Journal of Differential Equations》2004,204(2):439-470
We propose a direct method to control the first-order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T-direction and then second-order weak differentiability in the horizontal directions. 相似文献
7.
8.
We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies. In addition, we show that for every admissible parameter the problem has a smallest positive solution and we establish the monotonicity and continuity properties of the map . 相似文献
9.
Positive solutions for an elliptic equation in an annulus with a superlinear nonlinearity with zeros
We study existence, multiplicity, and the behavior, with respect to λ, of positive radially symmetric solutions of in annular domains in . The nonlinear term has a superlinear local growth at infinity, is nonnegative, and satisfies for a suitable positive and concave function a. For this, we combine several methods such as the sub and supersolutions method, a priori estimates and degree theory. 相似文献
10.
11.
Jacqueline Fleckinger Evans M. Harrell II François de Thélin 《Bulletin des Sciences Mathématiques》2007,131(7):613
It is shown that the fundamental eigenvalue ratio of the p-Laplacian is bounded by a quantity depending only on the dimension N and p. 相似文献
12.
Consider the Dirichlet problem for the parabolic equation
in
, where
$\Omega$ is a bounded domain in
and f has superlinear subcritical growth in u.
If f is independent of t and satisfies some
additional conditions then using a dynamical method we find multiple (three, six or infinitely many) nontrivial
stationary solutions. If f has the form
where m is periodic, positive and m,g satisfy some technical
conditions then we prove the existence of a positive periodic solution and
we provide a locally uniform bound for all global solutions. 相似文献
13.
In this article we prove existence of positive radially symmetric solutions for the nonlinear elliptic equation
14.
Michael E. Filippakis 《Journal of Differential Equations》2008,245(7):1883-1922
We consider a nonlinear elliptic equation driven by the p-Laplacian with Dirichlet boundary conditions. Using variational techniques combined with the method of upper-lower solutions and suitable truncation arguments, we establish the existence of at least five nontrivial solutions. Two positive, two negative and a nodal (sign-changing) solution. Our framework of analysis incorporates both coercive and p-superlinear problems. Also the result on multiple constant sign solutions incorporates the case of concave-convex nonlinearities. 相似文献
15.
Existence of multiple and sign-changing solutions for a problem involving p-Laplacian and jumping nonlinearities are considered via the construction of descent flow in . Sign-changing and multiple solutions are obtained under additional assumption on the nonlinearity. The uniqueness of positive (negative) solution theorem is included too. 相似文献
16.
Belkacem Said-Houari 《Journal of Differential Equations》2009,247(3):917-930
In this paper we consider the so-called p-system with linear damping, and we will prove an optimal decay estimates without any smallness conditions on the initial error. More precisely, if we restrict the initial data (V0,U0) in the space H3(R+)∩L1,γ(R+)×H2(R+)∩L1,γ(R+), then we can derive faster decay estimates than those given in [P. Marcati, M. Mei, B. Rubino, Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping, J. Math. Fluid Mech. 7 (2) (2005) 224-240; H. Zhao, Convergence to strong nonlinear diffusion waves for solutions of p-system with damping, J. Differential Equations 174 (1) (2001) 200-236] and [M. Jian, C. Zhu, Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant, J. Differential Equations 246 (1) (2009) 50-77]. 相似文献
17.
We consider the following nonlinear Schrödinger equations in Rn
18.
Mina Jiang 《Journal of Differential Equations》2009,246(1):50-2513
In this paper, we consider the so-called p-system with linear damping on quadrant. We show that for a certain class of given large initial data (v0(x),u0(x)), the corresponding initial-boundary value problem admits a unique global smooth solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically, at the Lp (2?p?∞) optimal decay rates, to the corresponding nonlinear diffusion wave which satisfies (1.9) provided the corresponding prescribed initial error function (V0(x),U0(x)) lies in (H3(R+)∩L1(R+))×(H2(R+)∩L1(R+)). 相似文献
19.
We consider the boundary value problem Δu+up=0 in a bounded, smooth domain Ω in R2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution up concentrating at exactly m points as p→∞. In particular, for a nonsimply connected domain such a solution exists for any given m?1. 相似文献
20.
In this paper, we successfully generalize the eigenvalue comparison theorem for the Dirichlet p -Laplacian (1<p<∞) obtained by Matei (2000) [19] and Takeuchi (1998) [22], respectively. Moreover, we use this generalized eigenvalue comparison theorem to get estimates for the first eigenvalue of the Dirichlet p-Laplacian of geodesic balls on complete Riemannian manifolds with radial Ricci curvature bounded from below w.r.t. some point. In the rest of this paper, we derive an upper and lower bound for the heat kernel of geodesic balls of complete manifolds with specified curvature constraints, which can supply new ways to prove the most part of two generalized eigenvalue comparison results given by Freitas, Mao and Salavessa (2013) [9]. 相似文献