共查询到20条相似文献,搜索用时 0 毫秒
1.
Benlong Xu 《Journal of Mathematical Analysis and Applications》2008,341(2):783-790
In this paper, we establish an exact multiplicity result of solutions for a class of semilinear elliptic equation. We also obtain a precise global bifurcation diagram of the solution set. As a result, an open problem presented by C.-H. Hsu and Y.-W. Shih [C.-H. Hsu, Y.-W. Shih, Solutions of semilinear elliptic equations with asymptotic linear nonlinearity, Nonlinear Anal. 50 (2002) 275-283] is completely solved. Our argument is mainly based on bifurcation theory and continuation method. 相似文献
2.
Pavel N. Ryabov 《Applied mathematics and computation》2010,217(7):3585-3590
The Kudryashov-Sinelshchikov equation for describing the pressure waves in liquid with gas bubbles is studied. New exact solutions of this equation are found. Modification of truncated expansion method is used for obtaining exact solution of this equation. 相似文献
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We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams. 相似文献
4.
Zhou Wen-Shu 《Journal of Mathematical Analysis and Applications》2008,346(1):107-119
In this paper we study existence and multiplicity of weak solutions of the homogenous Dirichlet problem for a singular semilinear elliptic equation with a quadratic gradient term. The proofs for the main results are based on a priori estimates of solutions of approximate problems. 相似文献
5.
In this paper, we study the global structure of the positive solutions to a logistic equation with constant yield harvesting under Neumann boundary value conditions. Moreover, we show that the logistic equation with the variable coefficients has exactly either zero, or one, or two solutions depending on the harvesting parameter. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Aly R. Seadawy 《Applied Mathematics Letters》2012,25(4):687-691
In the present study, we converted the resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrödinger (NLS) equation. Applying the function transformation method, the NLS equation was transformed to an ordinary differential equation, which depended only on one function ξ and can be solved. The general solution of the latter equation in ζ leads to a general solution of NLS equation. A new set of exact solutions for the two-dimensional NLS equation is obtained. 相似文献
8.
Kuo-Chih Hung 《Journal of Mathematical Analysis and Applications》2011,375(1):294-309
We study bifurcation diagrams of positive solutions for the p-Laplacian Dirichlet problem
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Radu Precup 《Journal of Mathematical Analysis and Applications》2009,352(1):48-56
Existence, localization and multiplicity results of positive solutions to a system of singular second-order differential equations are established by means of the vector version of Krasnoselskii's cone fixed point theorem. The results are then applied for positive radial solutions to semilinear elliptic systems. 相似文献
11.
We obtain precise global bifurcation diagrams for both one-sign and sign-changing solutions of a semilinear elliptic equation, for the nonlinearity being asymptotically linear. Our method combines the bifurcation approach and spectral analysis.
12.
Shingo Takeuchi 《Proceedings of the American Mathematical Society》2001,129(2):433-441
The degenerate elliptic equation with zero Dirichlet boundary condition, where is a positive parameter, and 0$">, is studied in three aspects: existence of maximal solution, -dependence of maximal solution and multiplicity of solutions.
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Anders Olofsson 《Journal of Mathematical Analysis and Applications》2003,283(2):375-385
We study the behavior at infinity of solutions of equations of the form Δu=up, where p>1, in dimensions n?3. In particular we extend results proved by Loewner and Nirenberg in Contribution to Analysis, 1974, pp. 245-272 for the case p=(n+2)/(n−2), n?3, to values of p in the range p>n/(n−2), n?3. 相似文献
15.
Yong-ping Sun 《高校应用数学学报(英文版)》2011,26(3):253-264
This paper investigates the boundary value problem for elastic beam equation of the form
u"(t) = q(t)f(t,u(t)u¢(t),u"(t),u"¢(t)),0 < t < 1,u'(t) = q(t)f(t,u(t)u'(t),u'(t),u'(t)),0 < t < 1, 相似文献
16.
We prove regularity and partial regularity results for finite Morse index solutions u∈H1(Ω)∩Lp(Ω) to the Lane-Emden equation −Δu=|u|p−1u in Ω. 相似文献
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This paper is devoted to the study of positive solutions of the semilinear elliptic equation Δu+K(|x|)u−p=0, x∈Rn with n?3 and p>0. Asymptotic behaviours of sky states and uniqueness of singular sky states are obtained via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has infinitely many positive solutions with fast growth. 相似文献
18.
By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained. 相似文献
19.
莫嘉琪 《高校应用数学学报(英文版)》2002,17(1):64-68
The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem,the asymptotic behavior of solution for the boundary value problem is studied. 相似文献
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We study the exact number of positive solutions of the Dirichlet problem for the one-dimensional prescribed mean curvature equation
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