共查询到20条相似文献,搜索用时 234 毫秒
1.
Donal ORegan Nikolaos S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4386-4392
In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory right hand side nonlinearity f(z,x). The hypothesis on f(z,x) does not imply the coercivity of the corresponding Euler functional. Using variational arguments and critical groups we show that the problem has at least two nontrivial smooth solutions. 相似文献
2.
J. Chabrowski 《Monatshefte für Mathematik》2002,137(4):261-272
We consider the nonlinear Schr?dinger equation
where W(x) = V(x) − E.
We establish the existence of the least energy solutions. We also formulate conditions guaranteeing the existence of multiple
solutions in terms of the Lusternik–Schnirelemann category.
Received March 30, 2001; in revised form May 29, 2002 相似文献
3.
带非局部源的退化半线性抛物方程的解的爆破性质 总被引:1,自引:0,他引:1
This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation
u
t
− (x
a
u
x
)
x
=∫
0
a
f(u)dx in (0,a) × (0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under
appropriate hypotheses, the global existence and blow-up in finite time of positve solutions are obtained. It is also proved
that the blow-up set is almost the whole domain. This differs from the local case. Furthermore, the blow-up rate is precisely
determined for the special case: f(u)=u
p
, p>1. 相似文献
4.
Jan Chabrowski Zhi-Qiang Wang 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):683-697
We consider the solvability of the Neumann problem for equation (1.1) in exterior domains in both cases: subcritical and critical.
We establish the existence of least energy solutions. In the subcritical case the coefficient
b(x) is allowed to have a potential well whose steepness is controlled by a parameter λ > 0. We show that least energy solutions
exhibit a tendency to concentrate to a solution of a nonlinear problem with mixed boundary value conditions. 相似文献
5.
We consider the Dirichlet problem for a class of quasilinear degenerate elliptic inclusions of the form ?div(𝒜(x, u, ?u)) + f(x)g(u) ∈ H(x, u, ?u), where 𝒜(x, u, ?u) is allowed to be degenerate. Without the general assumption that the multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz functions, we prove the existence of bounded solutions in weighed Sobolev space with the superlinear growth imposed on the nonlinearity g and the multifunction H(x, u, ?u) by using the Leray-Schauder fixed point theorem. Furthermore, we investigate the existence of extremal solutions and prove that they are dense in the solutions of the original system. Subsequently, a quasilinear degenerate elliptic control problem is considered and the existence theorem based on the proven results is obtained. 相似文献
6.
A.T. Lourêdo M. Milla Miranda 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7094-7110
We investigate the existence of local solutions of the following coupled system of Kirchhoff equations subject to nonlinear dissipation on the boundary: (∗) Here {Γ0,Γ1} is an appropriate partition of the boundary Γ of Ω and ν(x), the outer unit normal vector at x∈Γ1.By applying the Galerkin method with a special basis for the space where lie the approximations of the initial data, we obtain local solutions of the initial-boundary value problem for (∗). 相似文献
7.
The authors prove the existence of nontrivial solutions for the SchrSdinger equation -△u + V(x)u =λf(x, u) in R^N, where f is superlinear, subcritical and critical at infinity, respectively, V is periodic. 相似文献
8.
Shuguan Ji 《Calculus of Variations and Partial Differential Equations》2008,32(2):137-153
In this paper, we study the problem of time periodic solutions to the nonlinear wave equation with x-dependent coefficients on under the boundary conditions a
1
y(0, t)+b
1
y
x
(0, t) = 0, ( for i = 1, 2) and the periodic conditions y(x, t + T) = y(x, t), y
t
(x, t + T) = y
t
(x, t). Such a model arises from the forced vibrations of a bounded nonhomogeneous string and the propagation of seismic waves
in nonisotropic media. For , we establish the existence of time periodic solutions in the weak sense by utilizing some important properties of the wave
operator with x-dependent coefficients.
This work was supported by the 985 Project of Jilin University, the Specialized Research Fund for the Doctoral Program of
Higher Education, and the Science Research Foundation for Excellent Young Teachers of College of Mathematics at Jilin University. 相似文献
9.
This paper is devoted to the study of the following degenerate Neumann problem for a quasilinear elliptic integro-differential
operator Here is a second-order elliptic integro-differential operator of Waldenfels type and is a first-order Ventcel' operator with a(x) and b(x) being non-negative smooth functions on such that on . Classical existence and uniqueness results in the framework of H?lder spaces are derived under suitable regularity and structure
conditions on the nonlinear term f(x,u,Du).
Received April 22, 1997; in final form March 16, 1998 相似文献
10.
Yuji Liu 《Mediterranean Journal of Mathematics》2011,8(4):577-602
This article deals with a discrete type multi-point BVP of difference equations. The sufficient conditions to guarantee the
existence of at least three positive solutions are established. An example is presented to illustrate the main results. It
is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems
can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operators Δx(n) and Δx(n + 1). The difference concerned is a implicit difference equation. 相似文献
11.
P. Quittner W. Reichel 《Calculus of Variations and Partial Differential Equations》2008,32(4):429-452
Consider the equation −Δu = 0 in a bounded smooth domain , complemented by the nonlinear Neumann boundary condition ∂ν
u = f(x, u) − u on ∂Ω. We show that any very weak solution of this problem belongs to L
∞(Ω) provided f satisfies the growth condition |f(x, s)| ≤ C(1 + |s|
p
) for some p ∈ (1, p*), where . If, in addition, f(x, s) ≥ −C + λs for some λ > 1, then all positive very weak solutions are uniformly a priori bounded. We also show by means of examples that
p* is a sharp critical exponent. In particular, using variational methods we prove the following multiplicity result: if N ∈ {3, 4} and f(x, s) = s
p
then there exists a domain Ω and such that our problem possesses at least two positive, unbounded, very weak solutions blowing up at a prescribed point of
∂Ω provided . Our regularity results and a priori bounds for positive very weak solutions remain true if the right-hand side in the differential
equation is of the form h(x, u) with h satisfying suitable growth conditions. 相似文献
12.
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
13.
Bernhard Hein 《Calculus of Variations and Partial Differential Equations》2007,28(2):249-273
In
, n < 7, we treat the quasilinear, degenerate parabolic initial and boundary value problem which is the natural parabolic extension of Huisken and Ilmanen’s weak inverse mean curvature flow (IMCF). We prove long time existence and partial uniqueness of Lipschitz continuous weak solutions u(x,t) and show C
1,α-regularity for the sets ∂{x| u(x,t) < z }. Our approach offers a new approximation for weak solutions of the IMCF starting from a class of interesting and easily obtainable initial values; for these, the above sets are shown to converge against corresponding surfaces of the IMCF as t → ∞ globally in Hausdorff distance and locally uniformly with respect to the C
1,α-norm.Research partially supported by the DFG, SFB 382 at Tübingen University 相似文献
14.
Emilien Tarquini 《Monatshefte für Mathematik》2007,151(4):333-339
In this paper we consider the Gross-Pitaevskii equation iu
t
= Δu + u(1 − |u|2), where u is a complex-valued function defined on
, N ≥ 2, and in particular the travelling waves, i.e., the solutions of the form u(x, t) = ν(x
1 − ct, x
2, …, x
N
), where
is the speed. We prove for c fixed the existence of a lower bound on the energy of any non-constant travelling wave. This bound provides a non-existence
result for non-constant travelling waves of fixed speed having small energy. 相似文献
15.
Infinitely many solutions for indefinite quasilinear Schrödinger equations under broken symmetry situations 下载免费PDF全文
In this paper, we study the existence of infinitely many solutions for the indefinite quasilinear Schrödinger equations where α≥2, . When g(x,u) is only of locally superlinear growth at infinity in u and h(x,u) is not odd in u, the existence of infinitely many solutions is proved in spite of the lack of the symmetry of this problem by using dual approach and Bolle's perturbation method. Our results generalize some known results and are new even in the symmetric situation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
Global and periodic solutions for nonlinear wave equations with some localized nonlinear dissipation
Mitsuhiro Nakao 《Journal of Differential Equations》2003,190(1):81-107
We discuss the existence of global or periodic solutions to the nonlinear wave equation with the boundary condition , where Ω is a bounded domain in RN,ρ(x,v) is a function like ρ(x,v)=a(x)g(v) with g′(v)?0 and β(x,u) is a source term of power nonlinearity. a(x) is assumed to be positive only in a neighborhood of a part of the boundary ∂Ω and the stability property is very delicate, which makes the problem interesting. 相似文献
17.
In this paper, we deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problems where L(t) and W(t, x) are neither autonomous nor periodic in t. Our approach is variational and it is based on the critical point theory. We prove existence and multiplicity results of fast homoclinic solutions under general growth conditions on the potential function. Our theorems appear to be the first such result and our results extend some recent works. 相似文献
18.
Joanna M. Goard Philip Broadbridge Daniel J. Arrigo 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(6):926-942
The nonlinear diffusion equationu
t=[f(u)g(u
x
)] arises in recent models of turbulent transport and of stress dissipation in rock blasting. A Lie point symmetry analysis produces many similarity reductions of exponential and power-law forms, and reveals that for all choices off the equation is always integrable wheng(u
x
)=1/u
x
. We identify the functionsf(u) which guarantee equivalence to the linear heat equation. For all other choices off, the linear canonical form leads to a self-adjoint differential equation by separation of variablesx andt. We construct a number of explicit solutions with simple boundary conditions, which illustrate behavior in the vicinity of the degenerate region withu
x
=. If zero flux and constant concentration are maintained on free boundaries, then steep concentration gradients may evolve from smooth initial conditions. For other boundary conditions, unlike the examples of strong degeneracy, smoothing will occur at initial step discontinuities. 相似文献
19.
Positive ground state solutions for a class of Schrödinger–Poisson systems with sign‐changing and vanishing potential 下载免费PDF全文
Hongliang Liu Haibo Chen Qizhen Xiao 《Mathematical Methods in the Applied Sciences》2017,40(6):1937-1948
This paper deals with the following Schrödinger–Poisson systems where λ, ν are positive parameters and V(x) is sign‐changing and may vanish at infinity. Under some suitable assumptions, the existence of positive ground state solutions is obtained by using variational methods. Our main results unify and improve the recent ones in the literatures. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
20.
EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS 总被引:1,自引:0,他引:1
Du Zengji Lin Xiaojie Ge Weigao 《高校应用数学学报(英文版)》2005,20(3):323-330
This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method. 相似文献