aptitude questions with solutions for tcs

... [26–30], for elliptic systems with nonlinear boundary conditions see [31, 32], for the p-Laplacian with nonlinear boundary conditions of different type see [33–37], and for the p(x)-Laplacian with ... (x,t) t r 1 > 0 uniformly for x ∈ Ω 0 . (g 2 ) + There exists r 2 > 0 such that lim inf t→0 + G(x,t) t r 2 > 0 uniformly for x ∈ ∂Ω. Then (P ) has at least one nontrivial nonnegative solution with negative energy. Proof. ... upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann...

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... satisfied. Furthermore, by (3.23), for any u ẻ Z k with ||u|| ≤ r k , we have ϕ(u) ≥−cγ γ k  u  γ . Therefore, −cγ γ k ρ γ k ≤ inf u∈Z k ,  u  ≤ ρ k ϕ(u) ≤ 0 , so we have inf uZ k , u k (u) 0 for r k , g k đ ... inf |x|+ F( t, x) | x | Q uniformly for a.e. t ẻ [0, T]; (B4) F(t, x)=F(t,-x) for t ẻ [0, T] and all x in ℝ N . Then system (1.1) has infinite solution s u k in W 1,p ( t ) T for every positive integer ... Theo- rem 3.3, so system (1.1) has infinite solutions {u k }in W 1,p(t ) T for every positive integer k. Acknowledgements The authors thank the anonymous referees for valuable suggestions and comments...

Ngày tải lên: 20/06/2014, 22:20

... [(f) 0 - ε]||x||, for ||x|| r 3 , x ẻ P, t ẻ I. Therefore, for t Î I, x Î K,||x || c = r 3 , similar to (3.3), we have Tx ( t ) ≥ϕ (( Tu )( t )) ≥ λ[ ( ϕf ) 0 − ε]x c A ≥x c . Therefore,  Tx  c ≥  x  c , ... positive solutions for a class of p-Laplacian fourth-order differential equations w ith integral boundary conditions. By using Mawhin’ s continuat ion theorem, some sufficient conditions for the ... of solution for a class of second-order differential equations with integral boundary con- ditions at resonance are established in [8]. Feng et al. [9] considered the boundary value problems with one-dimensional...

Ngày tải lên: 21/06/2014, 00:20

... H + =0,thenweconsiderc j for j ≥ 2. As per the above arguments, J(0) < c 0 ≤ c 2 ≤ c 3 ≤···≤ c dim H − ≤ c ∞ and if c := c j = = c j+l for 2 ≤ j ≤ j + l ≤ dim H - with l ≥ 1, then i(K c ∩ S) ≥ l +1≥ 2. Therefore, ... theory with applications to differential equations. CBMS Reg Cof Ser Math. 65 (1986) doi:10.1186/1687-2770-2011-18 Cite this article as: Qian: Sign-changing solutions for some nonlinear problems with ... elliptic equation with strong resonance. Nonlinear Anal TMA. 66, 1885–1898 (2007). doi:10.1016/j.na.2006.02.046 6. Su, JB, Zhao, LG: An elliptic resonant problem with multiple solutions. J Math...

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... Song and Zhong [13], Wang [14]. For instance, Messaoudi [11] studied (1.2) for h(u t )=a|u t | m-2 u t and f(u)= b|u| p-2 u and proved a blow-up result for solutions with negative initial energy ... 2andaglobalresultfor2≤ p ≤ m. This result has been later improved by Mes- saoudi [12] to accommodate certain solutions with positive initial energy. Song and Zhong [13 ] considered (1.2) for h(u t )=-Δu t and ... uniform decay for nonlinear viscoelastic equation with strong damping. Math. Methods Appl. Sci. 24, 1043–1053 (2001). doi:10.1002/mma.250 2. Messaoudi, SA, Tatar, N-E: Global existence and uniform...

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... oscillations for classical Hamiltonian systems with bi-even subquadratic potentials. Nonlinear Anal. 24, 1665–1671 (1995). doi:10.1016/0362-546X(94)00227-9 6. Tang, CL: Periodic solutions for non-autonomous ... Periodic solutions for nonautonomous second order systems with sublinear nonlinearity. Proc Amer Math Soc. 126, 3263–3270 (1998). doi:10.1090/S0002-9939-98-04706-6 8. Tang, CL, Wu, XP: Periodic solutions ... for all n. Combining (3.4) with (3.5), we obtain C 4 h(| ¯ u n |) ≥ ⎛ ⎝ T  0 | ˙ u n (t ) | 2 dt ⎞ ⎠ 1/2 − C 5 (3:6) for all large n. By (3.1), (3.6), Lemma...

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... criterion and global weak solutions for Magnetohydrodynamics with zero viscosity. Discrete Contin Dyn Syst A. 25, 575–583 (2009) 27. Wu, J: Regularity results for weak solutions of the 3D MHD equations. ... scientists working with the hydrodynamic-fluid problems and phenomena. For more background, we ref er to [10] and references the rein. The e xis- tences of weak and strong solutions for micropolar ... smooth solutions for magneto-micropolar fluid equations with partial viscosity Yu-Zhu Wang * , Yifang Li and Yin-Xia Wang * Correspondence: yuzhu108@163. com School of Mathematics and Information...

Ngày tải lên: 21/06/2014, 01:20

... 2807–2813, 2010. 9 Y. Wang and W. Ge, “Periodic solutions for Duffing equations with a p-Laplacian-like operator,” Computers & Mathematics with Applications, vol. 52, no. 6-7, pp. 1079–1088, ... Article ID 736093, 11 pages doi:10.1155/2011/736093 Research Article Three Solutions for Forced Duffing-Type Equations with Damping Term Yongkun Li and Tianwei Zhang Department of Mathematics, ... distinct solutions for the following resonant Duffing-type equations with damping and perturbed term u  tσu  tft, ut  λgt, ut  pt,a.e.t ∈ 0,ω, u00  uω and without perturbed...

Ngày tải lên: 21/06/2014, 05:20

... The existence of positive solutions for two above cases received wide attention see 3–10. For example, Ji and Ge 4 studied the multiplicity of positive solutions for the multipoint boundary ... positive solutions for the one-dimensional p-Laplacian,” Proceedings of the American Mathematical Society, vol. 125, no. 8, pp. 2275–2283, 1997. 4 D. Ji and W. Ge, “Multiple positive solutions for ... one or two positive solutions for BVP1.1 is established by applying the Krasnoselskii fixed point theorem. In Section 4,we give the existence of three positive solutions for BVP1.1 by using...

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... solutions for fourth-order boundary value problems with three parameters,” Mathematical and Computer Modelling, vol. 46, no. 3-4, pp. 525–534, 2007. 8 H. Ma, “Symmetric positive solutions for ... 2010. 15 J. Zhao and W. Ge, “Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian,” Computers & Mathematics with Applications, vol. 58, no. 6, pp. 1103–1112, ... Applications,vol.67,no.5,pp. 1586–1598, 2007. 12 Y. Yang and J. Zhang, “Existence of solutions for some fourth-order boundary value problems with parameters,” Nonlinear Analysis. Theory, Methods & Applications,...

Ngày tải lên: 21/06/2014, 07:20

... B N 0; 1 has exactly two positive solutions for λ ∈ 0,λ 0  and has exactly one positive solution for λ  λ 0 and no positive solution exists for λ>λ 0 . For more general results of E λ involving sign-changing ... λ 0 > 0suchthatE λ  admits at least two positive solutions for all λ ∈ 0,λ 0  and has one positive solution for λ  λ 0 and no positive solution for λ>λ 0 . Actually, Adimurthi et al. 2, ... However, little has been done for this type of problem in unbounded domains. For Ω N , we are only aware of the works 12–15 which studied the existence of solutions for some related concave-convex...

Ngày tải lên: 21/06/2014, 11:20

... lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C 3 0, 1 as well as C 2 0, 1 positive solutions for fourth-order ... X. Zhang and L. Liu, “A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with p-Laplacian,” Nonlinear Analysis: Theory, Methods & Applications, ... author’s knowledge, there are no necessary and sufficient conditions available in the literature for the existence of solutions for integral boundary value problem 1.1 . Motivated by above papers, the purpose...

Ngày tải lên: 21/06/2014, 11:20

... ⊂ I j ∞ , such that lim l →∞ y l  t   ∞, uniformly for t ∈  α, β  . 3.33 Hence, we have lim l →∞ f  y l  t   y l  t   ∞, uniformly for t ∈  α, β  . 3.34 Now, we show that lim l ... structure of positive solutions of 1.1, 1.2 with f 0  ∞. However, to the best of our knowledge, there is no paper to discuss the global structure of nodal solutions of 1.1, 1.2 with f 0  ∞. In ... nodal solutions of 1.1, 1.2 under the following assumptions: A1 α i > 0fori  1, ,m− 2, with 0 <  m−2 i1 α i < 1; A2 f ∈ C 1 R \{0}, R ∩ CR, R satisfies fss>0fors / ...

Ngày tải lên: 21/06/2014, 11:20

... several researchers with the sphere of study ranging from the theoretical aspects of existence and uniqueness of solutions to the analytic and numerical methods for finding solutions. For some recent ... differential equations with three-point boundary conditions,” Computers & Mathematics with Applicationsl, vol. 58, no. 9, pp. 1838–1843, 2009. 16 Z. Bai and H. L ă u, Positive solutions for boundary ... denotes the Banach space of all continuous functions from 0, 1 → X endowed with a topology of uniform convergence with the norm denoted by ·. We remark that fractional boundary conditions...

Ngày tải lên: 21/06/2014, 16:20

... equations with maxima in complex domain, by using technique associated with measures of non-compactness. In this article, we establish the extreme solutions (maximal and minimal solutions) for fractional ... upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Extremal solutions for certain type of fractional differential equations with maxima Advances in ... R)−Carath´eodory with any decreasing growth function h ∈ L 1 (J, R + ) such that ∥F (t, u)∥ ≤ h(t) a.e t ∈ J for all u ∈ R. Therefore in view of Theorem 3.2, the problem (8) has maximal and minimal solutions. Example...

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