共查询到20条相似文献,搜索用时 375 毫秒
1.
We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a nonsmooth potential. Using the degree map for multivalued perturbations of (S)+-operators and the spectrum of a weighted eigenvalue problem for the scalar periodic p-Laplacian, we prove the existence of a strictly positive solution.
Michael E. Filippakis: Researcher supported by a grant of the National Scholarship Foundation of Greece (I.K.Y.) 相似文献
2.
Nikolaos S. Papageorgiou Francesca Papalini 《Journal of Fixed Point Theory and Applications》2009,5(1):157-184
We study a nonlinear periodic problem driven by the scalar p-Laplacian and having a nonsmooth potential (hemivariational inequality). Using a combination of variational techniques and
degree-theoretic methods based on a degree map for certain multivalued perturbations of (S)+operators, we establish the existence of two positive solutions. 相似文献
3.
This paper investigates 2m-th (m ≥ 2) order singular p-Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions
for sublinear 2m-th order singular p-Laplacian BVPs on closed interval. 相似文献
4.
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Proceedings Mathematical Sciences》2004,114(3):269-298
In this paper we study second order non-linear periodic systems driven by the ordinary vectorp-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth
critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function.
Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result
(even for smooth problems) for systems monitored by thep-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a
generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear
case the problem is at resonance at any eigenvalue. 相似文献
5.
Sergiu Aizicovici 《Journal of Mathematical Analysis and Applications》2011,375(1):342-364
We consider a nonlinear periodic problem, driven by the scalar p-Laplacian with a concave term and a Caratheodory perturbation. We assume that this perturbation f(t,x) is (p−1)-linear at ±∞, and resonance can occur with respect to an eigenvalue λm+1, m?2, of the negative periodic scalar p-Laplacian. Using a combination of variational techniques, based on the critical point theory, with Morse theory, we establish the existence of at least three nontrivial solutions. Useful in our considerations is an alternative minimax characterization of λ1>0 (the first nonzero eigenvalue) that we prove in this work. 相似文献
6.
D. Motreanu V. V. Motreanu N. S. Papageorgiou 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(5):535-557
We consider a nonlinear periodic problem driven by the scalar p-Laplacian, with an asymptotically (p?1)-linear nonlinearity. We permit resonance with respect to the second positive eigenvalue of the negative periodic scalar p-Laplacian and we assume nonuniform nonresonance with respect to the first positive eigenvalue. Using a combination of variational methods, with truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions. 相似文献
7.
In this paper we consider two nonlinear elliptic problems driven by the p-Laplacian and having a nonsmooth potential (hemivariational inequalities). The first is an eigenvalue problem and we prove
that if the parameter λ < λ2 = the second eigenvalue of the p-Laplacian, then there exists a nontrivial smooth solution. The second problem is resonant both near zero and near infinity
for the principal eigenvalue of the p-Laplacian. For this problem we prove a multiplicity result. Our approach is variational based on the nonsmooth critical point
theory. 相似文献
8.
In this paper we consider two nonlinear elliptic problems driven by the p-Laplacian and having a nonsmooth potential (hemivariational inequalities). The first is an eigenvalue problem and we prove
that if the parameter λ < λ2 = the second eigenvalue of the p-Laplacian, then there exists a nontrivial smooth solution. The second problem is resonant both near zero and near infinity
for the principal eigenvalue of the p-Laplacian. For this problem we prove a multiplicity result. Our approach is variational based on the nonsmooth critical point
theory.
Second author is Corresponding author. 相似文献
9.
Hua Su Baohe Wang Zhongli Wei Xiaoyan Zhang 《Journal of Mathematical Analysis and Applications》2007,330(2):836-851
In this paper, we study the existence of positive solutions for the nonlinear four-point singular boundary value problem for higher-order with p-Laplacian operator. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear singular boundary value problem with p-Laplacian operator are obtained. 相似文献
10.
Aboubakr Bayoumi 《Central European Journal of Mathematics》2005,3(1):76-82
We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from
l
p
into the scalar field, (0< p<1). This space is isomorphic to l
∞. 相似文献
11.
Kewei Zhang 《Frontiers of Mathematics in China》2008,3(4):599-642
We study the ‘universal’ strong coercivity problem for variational integrals of degenerate p-Laplacian type by mixing finitely many homogenous systems. We establish the equivalence between universal p-coercivity and a generalized notion of p-quasiconvex extreme points. We then give sufficient conditions and counterexamples for universal coercivity. In the case
of noncoercive systems we give examples showing that the corresponding variational integral may have infinitely many non-trivial
minimizers in W
01,p
which are nowhere C
1 on their supports. We also give examples of universally p-coercive variational integrals in W
01,p
for p ⩾ with L
∞ coefficients for which uniqueminimizers under affine boundary conditions are nowhere C
1.
相似文献
12.
F. Andreu J.M. Mazn J.D. Rossi J. Toledo 《Journal de Mathématiques Pures et Appliquées》2008,90(2):201-227
In this paper we study the nonlocal p-Laplacian type diffusion equation, If p>1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut=div(|u|p−2u) with homogeneous Neumann boundary conditions. We prove existence and uniqueness of a strong solution, and if the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in L∞(0,T;Lp(Ω)) to the solution of the p-Laplacian with homogeneous Neumann boundary conditions. The extreme case p=1, that is, the nonlocal analogous to the total variation flow, is also analyzed. Finally, we study the asymptotic behavior of the solutions as t goes to infinity, showing the convergence to the mean value of the initial condition. 相似文献
13.
The asymptotic behavior of the solutions for p-Laplacian equations as p → ∞ is studied. 相似文献
14.
Kwang Y. Kim 《Numerische Mathematik》2005,101(1):121-142
In this work we propose and analyze a mixed finite volume method for the p-Laplacian problem which is based on the lowest order Raviart–Thomas element for the vector variable and the P1 nonconforming element for the scalar variable. It is shown that this method can be reduced to a P1 nonconforming finite element method for the scalar variable only. One can then recover the vector approximation from the computed scalar approximation in a virtually cost-free manner. Optimal a priori error estimates are proved for both approximations by the quasi-norm techniques. We also derive an implicit error estimator of Bank–Weiser type which is based on the local Neumann problems.This work was supported by the Post-doctoral Fellowship Program of Korea Science & Engineering Foundation (KOSEF). 相似文献
15.
Sergiu Aizicovici 《Journal of Mathematical Analysis and Applications》2006,322(2):913-929
We study periodic problems driven by the scalar p-Laplacian with a multivalued right-hand side nonlinearity. We prove two existence theorems. In the first, we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p-Laplacian with periodic boundary conditions. In the second, we employ certain Landesman-Lazer type conditions. Our approach is based on degree theory. 相似文献
16.
17.
The authors study the p(x)-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f1 (x, u), f2(x, u) and h1(x), h2(x), such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces. 相似文献
18.
In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We
also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The
second is for systems and it is based on the nonsmooth local linking theorem. 相似文献
19.
JunNingZHAO QingYI 《数学学报(英文版)》2004,20(2):319-332
In this paper, we consider the generation and propagation of interfaces for p-Laplacian equations with the derivative of a bi-stable potential. 相似文献
20.
Heiko Gimperlein Matthias Maischak Elmar Schrohe Ernst P. Stephan 《Numerische Mathematik》2011,117(2):307-332
We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction,
where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational
inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements
based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational
problem in a suitable product of L
p
- and L
2-Sobolev spaces. 相似文献