共查询到20条相似文献,搜索用时 15 毫秒
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Oleksiy V. Kapustyan Pavlo O. Kasyanov Roman M. Taranets 《Journal of Mathematical Analysis and Applications》2021,493(2):124562
We prove local and global in time existence of non-negative weak solutions to the thin-film equation with absorption and obtain sufficient conditions for extra regularity of these solutions. Moreover, for the class of global strong solutions, we show existence of a trajectory attractor. 相似文献
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Gabriele Bonanno Giovanni Molica Bisci Vicenţiu D. Rădulescu 《Nonlinear Analysis: Theory, Methods & Applications》2012
In this paper, we are interested in the existence of infinitely many weak solutions for a non-homogeneous eigenvalue Dirichlet problem. By using variational methods, in an appropriate Orlicz–Sobolev setting, we determine intervals of parameters such that our problem admits either a sequence of non-negative weak solutions strongly converging to zero provided that the non-linearity has a suitable behaviour at zero or an unbounded sequence of non-negative weak solutions if a similar behaviour occurs at infinity. 相似文献
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SunFuqin WangMingxin 《偏微分方程(英文版)》2004,17(1):71-79
In this paper, we study the non-negative solutions to a degenerate parabolic system with nonlinear boundary conditions in the multi-dimensional case.By the upper and lower solutions method, we give the conditions on the existence and non-existence of global solutions. 相似文献
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In this paper, we present the local and global solutions of a system of hereditary and self-referred partial-differential
equations. Namely, by the assumption on the Lipschitz continuity of the initial conditions u
0, v
0, Theorem 1 states the existence of local solutions of the problem (1.3–1.4); furthermore, under the assumption that those
initial conditions are non-negative, non-decreasing, bounded, and lower semi-continuous functions, Theorem 2 gives global
solution which is also a non-negative, non-decreasing, bounded, and lower semi-continuous function (in variable x of even for any time t). 相似文献
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Dimitrios A. Kandilakis 《Journal of Differential Equations》2006,230(1):337-361
By using the fibering method, we study the existence of non-negative solutions for a class of indefinite quasilinear elliptic problems on unbounded domains with noncompact boundary, in the presence of competing subcritical and supercritical lower order nonlinearities. 相似文献
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Qi Zhang 《Transactions of the American Mathematical Society》1996,348(7):2811-2844
We obtain the existence of the weak Green's functions of parabolic equations with lower order coefficients in the so called parabolic Kato class which is being proposed as a natural generalization of the Kato class in the study of elliptic equations. As a consequence we are able to prove the existence of solutions of some initial boundary value problems. Moreover, based on a lower and an upper bound of the Green's function, we prove a Harnack inequality for the non-negative weak solutions.
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We consider quasilinear elliptic equations where the diffusion at each point depends on all the values of the solution in
a neighborhood of this point. The size of this neighborhood is parameterized by some non-negative number which represents
the range of nonlocal interactions. For fixed values of the parameter, the issue of the existence and local uniqueness of
the solution is addressed. In a radial symmetric setting, we give pointwise estimates of the solutions and prove the existence
of multiple solutions. Regarding bifurcation theory, we show that many local branches of solutions may exist while, among
them, only one is global and has no bifurcation point. 相似文献
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Lingju Kong 《中国科学 数学(英文版)》2019,(7)
We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived; in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results. 相似文献
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J. Chabrowski 《Annali di Matematica Pura ed Applicata》2007,186(4):703-719
In this paper we investigate the solvability of the nonlinear Neumann problem (1.1) with indefinite weight functions and a
critical Hardy–Sobolev nonlinearity. We examine the common effect of the shape of the graph of a weight function and the mean
curvature of the boundary on the existence of solutions of problem (1.1). We also investigate the regularity of solutions.
相似文献
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Summary In this paper a number of known results on the boundedness of solutions and the existence of periodic solutions of the scalar
equation 1.1(2) are extended to the vector equation 1.1(1). 相似文献
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我们利用Mawhin重合度拓展定理,研究了一类时滞三阶微分方程解的存在性问题,得到了其存在2π周期解的新的结果.值得关注的是,我们允许滞量r是一个函数,并且所得结论与时滞ι(t)有关.同时给出一个实例来论证我们的结果. 相似文献
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Rong Cheng 《Applicable analysis》2017,96(5):778-798
In this paper, we study the existence and concentration of positive solution of a class of coupled Schrödinger equations. We admit that the potentials may not be non-negative and suppose that the intersection of the sets has positive Lebesgue measure. By studying the modified functional of the associated functional carefully, we establish the existence of positive least energy solutions for the coupled Schrödinger system. Moreover, we prove the concentration phenomenon of the positive solution when the parameter goes to infinity. 相似文献
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严国政 《数学物理学报(B辑英文版)》1997,(1)
1IntroductionInthispapertweconsiderthefollowingsystemswithinitialvaluewhereu=(tLt,'',Wi),F=(FI,'.',Fn),t20,--co0,thereisasolutionu(x,f)of(1.1),suchthatIIullHI5C(T).C(T)isaconstantdependingboundlyon"o(z)andT.Ifb=0,then(1.l)isthetypicalselnilinearheatsystems,i.e.therearemugpapersdealingwiththesystems(1.3).Theinvestigationill… 相似文献
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Yihong Song Jingsong Ni Christopher T.H. Baker 《Journal of Difference Equations and Applications》2013,19(3):423-439
The existence of non-negative convergent solutions of discrete Volterra equations is obtained, by using a variety of fixed-point theorems. Examples are given to illustrate the results. 相似文献
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H. Bereketoglu 《Periodica Mathematica Hungarica》1992,24(1):13-22
The aim of this paper is to investigate sufficient conditions (Theorem 1) for the nonexistence of nontrivial periodic solutions
of equation (1.1) withp ≡ 0 and (Theorem 2) for the existence of periodic solutions of equation (1.1). 相似文献
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We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. Under suitable conditions, the comparison properties of solutions are proved. Those results are applied to construct continuous state branching processes with immigration as strong solutions of stochastic equations. 相似文献
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In this paper, we study the integrability of the non-negative solutions to the Euler-Lagrange equations associated with Weighted Hardy-Littlewood-Sobolev (HLS) inequality. We obtain the optimal integrability for the solutions. The integrability and the radial symmetry (which we derived in our earlier paper) are the key ingredients to study the growth rate at the center and the decay rate at infinity of the solutions. These are also the essential properties needed to classify all non-negative solutions. Some simple generalizations are also provided here. 相似文献