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1.
Hideo Deguchi 《Monatshefte für Mathematik》2009,156(3):211-231
This paper is devoted to the study of the initial value problem for parabolic systems with discontinuous nonlinearities from
the viewpoint of the existence, uniqueness and stability of weak solutions. Also the relationship with the solutions of the
corresponding differential inclusions is studied.
相似文献
2.
Salvatore A. Marano 《Proceedings of the American Mathematical Society》1997,125(10):2953-2961
For a family of elliptic eigenvalue problems with highly discontinuous nonlinearities, the existence of unbounded continua of positive solutions containing (0,0) is established by using techniques and results from set-valued analysis. Some special cases are then presented and discussed.
3.
Jorge Aragona Antnio Ronaldo Gomes Garcia Stanley Orlando Juriaans 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5187-5207
In [H. Brézis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73–97.] Brézis and Friedman prove that certain nonlinear parabolic equations, with the δ-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186–196.] Colombeau and Langlais prove that these equations have a unique solution even if the δ-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais’ result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371–399.]. 相似文献
4.
In this paper, we study the asymptotic behavior of solutions of non-autonomous parabolic problems with singular initial data. We first establish the well-posedness of the equation when the initial data belongs to Lr(Ω) (1<r<∞) and W1,r(Ω) (1<r<N), respectively. When the initial data belongs to Lr(Ω), we establish the existence of uniform attractors in Lr(Ω) for the family of processes with external forces being translation bounded but not translation compact in . When we consider the existence of uniform attractors in , the solution of equation lacks the higher regularity, so we introduce a new type of solution and prove the existence result. For the long time behavior of solutions of the equation in W1,r(Ω), we only obtain the uniform attracting property in the weak topology. 相似文献
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This is a subsequent work of our previous one in [25]. Let the nonlinear terms of non-autonomous parabolic problems with singular initial data satisfy subcritical and critical growth conditions. We first establish the existence of uniform attractors in W1,r(Ω), 1<r<N, for the family of processes corresponding to the equations with external forces being translation bounded but not translation compact. Then, we prove the existence of pullback attractors in Lr(Ω) and W1,r(Ω), respectively, for the process corresponding to the equation with the weaker assumption on the external force than previous one. Finally, we investigate the robust of attractors and establish the existence of pullback exponential attractors for the process acting in Lr(Ω) and W1,r(Ω), respectively. 相似文献
8.
V. N. Pavlenko 《Differential Equations》2016,52(4):505-516
We study the problem of finding time-periodic solutions of a parabolic equation with the homogeneous Dirichlet boundary condition and with a discontinuous nonlinearity. We assume that the nonlinearity is equal to the difference of two superpositionally measurable functions nondecreasing with respect to the state variable. For such a problem, we prove the principle of lower and upper solutions for the existence of strong solutions without additional constraints on the “jumping-up” discontinuities in the nonlinearity. We obtain existence theorems for strong solutions of this class of problems, including theorems on the existence of two nontrivial solutions. 相似文献
9.
In this study, the Fučik spectrum is used to investigate Kirchhoff-type problems with jumping nonlinearities at infinity, and a new result on the existence of nontrivial solutions is obtained. 相似文献
10.
In this paper, Fucik spectrum, ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear
elliptic boundary value problems with jumping nonlinearities at zero or infinity, and some new results on the existence of
nontrivial solutions, multiple solutions and sign-changing solutions are obtained. In one case seven nontrivial solutions
are got. The techniques have independent interest. 相似文献
11.
D. Nomirovskii 《Journal of Differential Equations》2007,233(1):1-21
We consider the following linear parabolic system in a domain with a thin low-permeable insertion (“imperfect interface”):
12.
Using a three critical points theorem for nondifferentiable functionals, we investigate a class of second order difference equation with discontinuous nonlinearities. A new multiplicity result is obtained. 相似文献
13.
In this paper, we study the effect of domain shape on the number of 2-nodal solutions for the semilinear elliptic equation involving non-odd nonlinearities. We prove that a semilinear elliptic equation in an m-bump domain (possibly unbounded) has m2 2-nodal solutions and we can find a least energy nodal solution in those solutions. Furthermore, we can describe the bump location of these solutions. 相似文献
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研究了一类非线性演化方程初值问题.通过不变子空间方法,这类初值问题被约化为常微分方程组的初值问题.这类初值问题是适定的.本文给出了这类初值问题关于时间变量t的幂级数解. 相似文献
17.
We deal with the existence of periodic solutions for problems with a jump discontinuity. We use an approximation procedure and the method of the lower and upper solutions. 相似文献
18.
Inverse nodal and inverse spectral problems are studied for second-order differential operators on a finite interval with discontinuity conditions inside the interval. Uniqueness theorems are proved, and a constructive procedure for the solution is provided. 相似文献
19.
BOUNDARY VALUE PROBLEMS FOR A CLASS OF QUASILINEAR DIFFERENTIAL SYSTEMS WITH SINGULAR NONLINEARITIES
GUOZONGMING YANGZUODONG 《高校应用数学学报(英文版)》1998,13(2):123-134
In this paper the existence and multiplicities of positive solutions for a class of quasiliear differential systems with singular nonlinearities via Leray-Schaudet degree theory are established. 相似文献
20.
We obtain positive solutions of singular p-Laplacian problems with sign changing nonlinearities using variational methods. 相似文献