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《Nonlinear Analysis: Theory, Methods & Applications》2005,60(2):221-230
In this paper, we consider the existence of multiple nontrivial solutions for some fourth order semilinear elliptic boundary value problems. The weak solutions are sought by means of Morse theory and local linking. 相似文献
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Using the minimax methods in critical point theory and a generalized Landesman-Lazer type condition, we obtain two solutions for a class of semilinear elliptic equations near resonance at higher eigenvalues. 相似文献
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Multiplicity results for semilinear elliptic equations are obtained under one-sided growth conditions on the nonlinearity. Techniques of nonsmooth critical point theory are employed. 相似文献
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In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations −△u+a(x)u=g(x,u) in a bounded smooth domain of RN(N≥3) with the Dirichlet boundary value, where the primitive of the nonlinearity g is of superquadratic growth near infinity in u and the potential a is allowed to be sign-changing. Recent results in the literature are generalized and significantly improved. 相似文献
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Huei-li Lin 《Journal of Mathematical Analysis and Applications》2012,391(1):107-118
This article investigates the effect of the coefficient of the critical nonlinearity. For sufficiently small , there are at least k positive solutions of the semilinear elliptic systems where is a bounded domain, , and for . 相似文献
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Xiao-Jiao HuangXing-Ping Wu Chun-Lei Tang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2602-2611
The existence and multiplicity of positive solutions are obtained for a class of semilinear elliptic equations with critical weighted Hardy-Sobolev exponents and the concave-convex nonlinearity by variational methods and some analysis techniques. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2005,62(3):455-465
The multiplicity results are obtained for solutions of the Neumann problem for nonlinear elliptic equations with unbounded nonlinearity by the Implicit Function Theorem and the Morse theory. 相似文献
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Francesca Alessio Piero Montecchiari 《Calculus of Variations and Partial Differential Equations》2007,30(1):51-83
We consider a class of semilinear elliptic equations of the form
where is a periodic, positive function and is modeled on the classical two well Ginzburg-Landau potential . We show, via variational methods, that if the set of solutions to the one dimensional heteroclinic problem
has a discrete structure, then (0.1) has infinitely many solutions periodic in the variable y and verifying the asymptotic conditions as uniformly with respect to .
Supported by MURST Project ‘Metodi Variazionali ed Equazioni Differenziali Non Lineari’. 相似文献
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Francesca Alessio Piero Montecchiari 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):1317-1346
This paper concerns the existence and asymptotic characterization of saddle solutions in ${\mathbb {R}^{3}}$ for semilinear elliptic equations of the form $$-\Delta u + W'(u) = 0,\quad (x, y, z) \in {\mathbb {R}^{3}} \qquad\qquad\qquad (0.1)$$ where ${W \in \mathcal{C}^{3}(\mathbb {R})}$ is a double well symmetric potential, i.e. it satisfies W(?s) = W(s) for ${s \in \mathbb {R},W(s) > 0}$ for ${s \in (-1,1)}$ , ${W(\pm 1) = 0}$ and ${W''(\pm 1) > 0}$ . Denoted with ${\theta_{2}}$ the saddle planar solution of (0.1), we show the existence of a unique solution ${\theta_{3} \in {\mathcal{C}^{2}}(\mathbb {R}^{3})}$ which is odd with respect to each variable, symmetric with respect to the diagonal planes, verifies ${0 < \theta_{3}(x,y,z) < 1}$ for x, y, z > 0 and ${\theta_{3}(x, y, z) \to_{z \to + \infty} \theta_{2}(x, y)}$ uniformly with respect to ${(x, y) \in \mathbb {R}^{2}}$ . 相似文献
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Jing Zhang Shujie Li Yuwen Wang Xiaoping Xue 《Journal of Mathematical Analysis and Applications》2010,371(2):682-690
We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l>2 and (IIl), l?1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions. 相似文献
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In this paper, we consider the existence of multiple positive solutions for an inhomogeneous critical semilinear elliptic problem. We show that the problem possesses at least four positive solutions. 相似文献
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In this paper, we study the following semilinear elliptic system where N > 2, f(x,t) and g(x,t) are continuous functions and satisfy additional conditions. By using critical point theory of strongly indefinite functionals, we obtain a positive ground state solution and infinitely many geometrically distinct solutions when f(x,t) and g(x,t) are periodic in X and odd in t. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献