A Knobloch-type result for p(t)-Laplacian systems☆
By Xianling Fan, Xinghao Fan. 2003
61 citations recorded by the source corpus.
We consider the periodic boundary value problem of ordinary differential systems with p(t)-Laplacian of the form |u′|p(t)−2u′′=f(t,u),u(0)−u(T)=u′(0)−u′(T)=0, where p∈C(R,R) is a T-periodic function and p(t)>1 for t∈R, f∈C(R×RN,RN) and f(t,u) is T-periodic with respect to t. We prove that, if there exists some r>0 such that 〈f(t,u),u〉⩾0 for t∈R and u∈RN with |u|=r, then the problem has at least one solution u satisfying |u(t)|⩽r for t∈R. This is a generalization of the results obtained by Knobloch and Mawhin under the case of p(t)≡2 and p(t)≡p∈(1,∞) respectively.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c0bbf2d45d35452ca533cb1b0bc5844acd6677b2
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Citations in the corpus
- Chapter 7 Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations (2006, unknown): “[67], [68]).”
- Overview of differential equations with non-standard growth (2010, unknown): “Fan [92] considered the boundary value problem of ordinary differential systems {( |u′|p(x)−2u′ )′ = g(x, u), x ∈ I, u(0)− u(T ) = u′(0)− u′(T ) = 0, (3.”
- Solvability of Nonlinear Singular Problems for Ordinary Differential Equations (2009, unknown): “Fan [87], Fan et al.”
- Existence and multiplicity results for a newp(x)-Kirchhoff problem (2019, background): “emburgnorm kuk Lp(x)(Ω) = |u| p(.) = inf ( µ>0; Z Ω u(x) µ p(x) dx ≤ 1 ) , which is a separable and reflexive Banach space. For basic properties of the variable exponent Lebesgue spaces we refer to [20, 25, 39]. 4 Proposition2.1 ([39]). The space (Lp(x)(Ω),|.| p(x)) is separable, uniformly convex,”