共查询到20条相似文献,搜索用时 125 毫秒
1.
Dumitru Motreanu 《Journal of Differential Equations》2010,249(12):3352-3376
By variational methods, we prove the existence of a sign-changing solution for the p-Laplacian equation under Dirichlet boundary condition with jumping nonlinearity having relation to the Fu?ík spectrum of p-Laplacian. We also provide the multiple existence results for the p-Laplacian problems. 相似文献
2.
Nikolaos Halidias 《Bulletin des Sciences Mathématiques》2003,127(6):549-556
We consider a class of noncoercive hemivariational inequalities involving the p-Laplacian. Our goal is to obtain the existence of a nontrivial solution. Using the mountain-pass theorem for locally Lipschitz functionals we obtain the desired result. 相似文献
3.
We state and prove a general Harnack inequality for minimizers of nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian. 相似文献
4.
Maria Michaela Porzio 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5359-5382
We prove existence, uniqueness, regularity results and estimates describing the behavior (both for large and small times) of a solution u of some nonlinear parabolic equations of Leray-Lions type including the p-Laplacian. In particular we show how the summability of the initial datum u0 and the value of p influence the behavior of the solution u, producing ultracontractive or supercontractive estimates or extinction in finite time or different kinds of decay estimates. 相似文献
5.
Yuri Bozhkov 《Journal of Differential Equations》2003,190(1):239-267
By using the fibering method introduced by Pohozaev, we prove existence of multiple solutions for a Diriclhlet problem associated to a quasilinear system involving a pair of (p,q)-Laplacian operators. 相似文献
6.
We consider the Orlicz-growth generalization to the evolutionary p-Laplacian and to the evolutionary symmetric p-Laplacian. We derive the spatial second-order Caccioppoli-type estimate for a local weak solution to these systems. Our result is new even for the p-case. 相似文献
7.
We study qualitative and quantitative properties of local weak solutions of the fast p-Laplacian equation, t∂u=Δpu, with 1<p<2. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of Rn×[0,T]. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion range, that is when 1<p?2n/(n+1). The boundedness results may be also extended to the limit case p=1, while the positivity estimates cannot.We prove the existence as well as sharp asymptotic estimates for the so-called large solutions for any 1<p<2, and point out their main properties.We also prove a new local energy inequality for suitable norms of the gradients of the solutions. As a consequence, we prove that bounded local weak solutions are indeed local strong solutions, more precisely . 相似文献
8.
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
9.
We study the Hölder regularity of weak solutions to the evolutionary p -Laplacian system with critical growth on the gradient. We establish a natural criterion for proving that a small solution and its gradient are locally Hölder continuous almost everywhere. Actually our regularity result recovers the classical result in the case p=2 [16] and can be applied to study the regularity of the heat flow for m-dimensional H-systems as well as the m-harmonic flow. 相似文献
10.
Kanishka Perera Martin Schechter 《Journal of Mathematical Analysis and Applications》2009,358(2):485-1936
We solve boundary value problems for p-Laplacian systems using sandwich pairs. 相似文献
11.
Dumitru Motreanu 《Journal of Differential Equations》2007,232(1):1-35
In this paper we examine semilinear and nonlinear Neumann problems with a nonsmooth locally Lipschitz potential function. Using variational methods based on the nonsmooth critical point theory, for the semilinear problem we prove a multiplicity result under conditions of double resonance at higher eigenvalues. Our proof involves a nonsmooth extension of the reduction method due to Castro-Lazer-Thews. The nonlinear problem is driven by the p-Laplacian. So first we make some observations about the beginning of the spectrum of (−Δp,W1,p(Z)). Then we prove an existence and multiplicity result. The existence result permits complete double resonance. The multiplicity result specialized in the semilinear case (i.e. p=2) corresponds to the super-sub quadratic situation. 相似文献
12.
Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem
Constantin P. Niculescu Ionel Roven?a 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):270-277
In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for p-Laplacian, has finite time blow-up solutions. 相似文献
13.
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
14.
Leonelo Iturriaga Eugenio Massa Justino Sánchez Pedro Ubilla 《Journal of Differential Equations》2010,248(2):309-327
Using a combination of several methods, such as variational methods, the sub and supersolutions method, comparison principles and a priori estimates, we study existence, multiplicity, and the behavior with respect to λ of positive solutions of p-Laplace equations of the form −Δpu=λh(x,u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x,a(x))=0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. 相似文献
15.
M. Arias J. Campos M. Cuesta J.-P. Gossez 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2008
We prove the existence of a first nonprincipal eigenvalue for an asymmetric Neumann problem with weights involving the p-Laplacian (cf. (1.2) below). As an application we obtain a first nontrivial curve in the corresponding Fu?ik spectrum (cf. (1.4) below). The case where one of the weights has meanvalue zero requires some special attention in connexion with the (PS) condition and with the mountain pass geometry. 相似文献
16.
Roberta Filippucci 《Journal of Differential Equations》2011,250(1):572-595
In this paper we deal with noncoercive elliptic systems of divergence type, that include both the p-Laplacian and the mean curvature operator and whose right-hand sides depend also on a gradient factor. We prove that any nonnegative entire (weak) solution is necessarily constant. The main argument of our proofs is based on previous estimates, given in Filippucci (2009) [12] for elliptic inequalities. Actually, the main technique for proving the central estimate has been developed by Mitidieri and Pohozaev (2001) [23] and relies on the method of test functions. No use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required. 相似文献
17.
Jingxue Yin 《Journal of Differential Equations》2007,237(2):421-445
The paper concerns the well-posedness problem of an evolutionary weighted p-Laplacian with boundary degeneracy. Different from the classical theory for linear equations, it is shown that the degenerate portion of the boundary should be decomposed into two parts: the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics. We formulate reasonably the boundary value condition and establish the existence and uniqueness theorems. 相似文献
18.
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
19.
Jorge Cossio Sigifredo Herrón 《Journal of Mathematical Analysis and Applications》2008,345(1):583-592
We prove that an asymptotically linear Dirichlet problem which involves the p-Laplacian operator has multiple radial solutions when the nonlinearity has a positive zero and the range of the ‘p-derivative’ of the nonlinearity includes at least the first j radial eigenvalues of the p-Laplacian operator. The main tools that we use are a uniqueness result for the p-Laplacian operator and bifurcation theory. 相似文献
20.
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