... [26–30], for elliptic systems with nonlinearboundary conditions see [31, 32], for the p-Laplacian with nonlinear boundaryconditions of different type see [33–37], and for the p(x)-Laplacian with ... (x,t)tr1>0 uniformly for x ∈ Ω0.(g2)+There exists r2> 0 such that lim inft→0+G(x,t)tr2> 0 uniformly for x ∈ ∂Ω.Then (P ) has at least one nontrivial nonnegative solution with negativeenergy.Proof. ... upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.Existence and multiplicity of solutionsfor nonlocal p(x)-Laplacian equations with nonlinear Neumann...
... by (3.23), for any u Î Zk with ||u|| ≤ rk, we haveϕ(u) ≥−cγγkuγ.Therefore,−cγγkργk≤ infu∈Zk,u≤ρkϕ(u) ≤ 0,so we haveinfu∈Zk,u≤ρkϕ(u) →0 for rk, ... x)|x|μ≥ Quniformly for a.e. t Î [0, T];(B4) F(t, x)=F(t,-x) for t Î [0, T] and all x in ℝN.Then system (1.1) has infinite solution s ukinW1,p(t)T for every positive integer ... Theo-rem 3.3, so system (1.1) has infinite solutions {uk}inW1,p(t)T for every positive integer k.AcknowledgementsThe authors thank the anonymous referees for valuable suggestions and comments...
... [(f)0- ε]||x||, for ||x|| ≤ r3, x Î P, t Î I.Therefore, for t Î I, x Î K,||x ||c= r3, similar to (3.3), we haveTx(t)≥ϕ((Tu)(t))≥ λ[(ϕf)0− ε]xcA ≥xc.Therefore,Txc≥xc, ... positive solutionsfor a class of p-Laplacianfourth-order differential equations w ith integral boundary conditions. By usingMawhin’ s continuat ion theorem, some sufficient conditions for the ... ofsolution 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 boundaryvalue problems with one-dimensional...
... H+=0,thenweconsidercj for j ≥ 2. As per the above arguments,J(0) < c0≤ c2≤ c3≤···≤ cdim H−≤ c∞and if c := cj= = cj+l for 2 ≤ j ≤ j + l ≤dim H- with l ≥ 1, then i(Kc∩ S) ≥ l +1≥ 2.Therefore, ... theory with applications to differential equations. CBMS Reg Cof SerMath. 65 (1986)doi:10.1186/1687-2770-2011-18Cite this article as: Qian: Sign-changing solutionsfor some nonlinear problems with ... elliptic equation with strong resonance. Nonlinear Anal TMA. 66, 1885–1898 (2007).doi:10.1016/j.na.2006.02.0466. Su, JB, Zhao, LG: An elliptic resonant problem with multiple solutions. J Math...
... Song and Zhong [13],Wang [14]. For instance, Messaoudi [11] studied (1.2) for h(ut)=a|ut|m-2utand f(u)=b|u|p-2u and proved a blow-up result forsolutionswith negative initial energy ... 2andaglobalresultfor2≤ p ≤ m. This result has been later improved by Mes-saoudi [12] to accommodate certain solutionswith positive initial energy. Song andZhong [13 ] considered (1.2) for h(ut)=-Δutand ... uniform decay for nonlinear viscoelastic equation with strong damping. Math. Methods Appl. Sci. 24, 1043–1053 (2001). doi:10.1002/mma.2502. Messaoudi, SA, Tatar, N-E: Global existence and uniform...
... oscillations for classical Hamiltonian systems with bi-even subquadratic potentials. Nonlinear Anal.24, 1665–1671 (1995). doi:10.1016/0362-546X(94)00227-96. Tang, CL: Periodic solutionsfor non-autonomous ... Periodic solutionsfor nonautonomous second order systems with sublinear nonlinearity. Proc Amer MathSoc. 126, 3263–3270 (1998). doi:10.1090/S0002-9939-98-04706-68. Tang, CL, Wu, XP: Periodic solutions ... for all n. Combining (3.4) with (3.5), we obtainC4h(|¯un|) ≥⎛⎝T0|˙un(t ) |2dt⎞⎠1/2− C5(3:6) for all large n. By (3.1), (3.6), Lemma...
... criterion and global weak solutionsfor Magnetohydrodynamics with zero viscosity. Discrete ContinDyn 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 andphenomena. For more background, we ref er to [10] and references the rein. The e xis-tences of weak and strong solutionsfor micropolar ... smooth solutions for magneto-micropolar fluid equations with partialviscosityYu-Zhu Wang*, Yifang Li and Yin-Xia Wang* Correspondence: yuzhu108@163.comSchool of Mathematics andInformation...
... 2807–2813,2010.9 Y. Wang and W. Ge, “Periodic solutionsfor Duffing equations with a p-Laplacian-like operator,”Computers & Mathematics with Applications, vol. 52, no. 6-7, pp. 1079–1088, ... Article ID 736093, 11 pagesdoi:10.1155/2011/736093Research ArticleThree Solutionsfor Forced Duffing-TypeEquations with Damping TermYongkun Li and Tianwei ZhangDepartment of Mathematics, ... distinct solutionsfor the following resonant Duffing-type equations with damping andperturbed term utσutft, ut λgt, ut pt,a.e.t ∈ 0,ω, u00 uω andwithout perturbed...
... The existence of positive solutions for two above cases received wide attention see 3–10. For example, Ji and Ge 4 studiedthe multiplicity of positive solutionsfor the multipoint boundary ... positive solutionsfor the one-dimensional p-Laplacian,” Proceedings of theAmerican Mathematical Society, vol. 125, no. 8, pp. 2275–2283, 1997.4 D. Ji and W. Ge, “Multiple positive solutionsfor ... one or two positive solutions for BVP1.1 is established by applying the Krasnoselskii fixed point theorem. In Section 4,wegive the existence of three positive solutionsfor BVP1.1 by using...
... solutionsfor fourth-order boundary valueproblems with three parameters,” Mathematical and Computer Modelling, vol. 46, no. 3-4, pp. 525–534,2007.8 H. Ma, “Symmetric positive solutionsfor ... 2010.15 J. Zhao and W. Ge, “Positive solutionsfor a higher-order four-point boundary value problem with ap-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 solutionsfor some fourth-order boundary value problems with parameters,” Nonlinear Analysis. Theory, Methods & Applications,...
... BN0; 1has exactly two positive solutionsfor λ ∈ 0,λ0 and has exactly one positive solution for λ λ0and no positive solution exists for λ>λ0. For more general results of Eλinvolvingsign-changing ... λ0> 0suchthatEλ admits atleast two positive solutionsfor all λ ∈ 0,λ0 and has one positive solution for λ λ0and nopositive solution for λ>λ0. Actually, Adimurthi et al. 2, ... However, little has been done for this type of problem in unboundeddomains. For ΩN, we are only aware of the works 12–15 which studied the existenceof solutionsfor some related concave-convex...
... lower solutions method together with maximal principle, we establish anecessary and sufficient condition for the existence of pseudo-C30, 1 as well as C20, 1 positive solutions for fourth-order ... X. Zhang and L. Liu, “A necessary and sufficient condition for positive solutionsfor fourth-ordermulti-point boundary value problems with p-Laplacian,” Nonlinear Analysis: Theory, Methods &Applications, ... author’sknowledge, there are no necessary and sufficient conditions available in the literature for theexistence of solutionsfor integral boundary value problem 1.1 . Motivated by above papers,the purpose...
... ⊂ Ij∞, suchthatliml →∞ylt ∞, uniformly for t ∈α, β. 3.33Hence, we haveliml →∞fyltylt ∞, uniformly for t ∈α, β. 3.34Now, we show that liml ... structure of positive solutions of 1.1, 1.2 with f0 ∞. However, to the best of our knowledge, there is no paperto discuss the global structure of nodal solutions of 1.1, 1.2 with f0 ∞.In ... nodal solutions of 1.1, 1.2 under the following assumptions:A1 αi> 0fori 1, ,m− 2, with 0 <m−2i1αi< 1;A2 f ∈ C1R \{0}, R ∩ CR, R satisfies fss>0fors/...
... severalresearchers with the sphere of study ranging from the theoretical aspects of existence anduniqueness of solutions to the analytic and numerical methods for finding solutions. For somerecent ... differentialequations with three-point boundary conditions,” Computers & Mathematics with Applicationsl, vol. 58,no. 9, pp. 1838–1843, 2009.16 Z. Bai and H. L¨u, “Positive solutionsfor boundary ... denotes the Banach space of all continuous functions from 0, 1 → Xendowed with a topology of uniform convergence with the norm denoted by ·.We remark that fractional boundary conditions...
... equations with maxima in complex domain, byusing technique associated with measures of non-compactness.In this article, we establish the extreme solutions (maximal and minimal solutions) for fractional ... upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.Extremal solutionsfor certain type of fractional differential equations with maximaAdvances in ... R)−Carath´eodory with any decreasing growth function h ∈L1(J, R+) such that ∥F (t, u)∥ ≤ h(t) a.e t ∈ J for all u ∈ R. Therefore in view of Theorem3.2, the problem (8) has maximal and minimal solutions. Example...