The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(...This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(u)u - beta integral (u)(0) g(s)ds is unbounded, a(x) is a Holder continuous function which changes sign on Omega and integral (Omega-) \a(x)\ dx is suitably small. The authors prove the existence of a nonnegative nontrivial solution for N > p > 1. in particular, the existence of a positive solution to the problem for N > p greater than or equal to 2. Our main theorem generalizes a recent result of Samia Khanfir and Leila Lassoued (see [1]) concerning the case where p = 2. They prove also that if g(u) = \u \ (q-2)u with p < q < p* and Omega (+) = {x is an element ofQ \a(x) > 0} is a nonempty open set, then the above problem possesses infinitely many solutions.展开更多
In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bound...In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases:(i) Both q and r are subcritical;(ii) r is critical and q is subcritical;(iii) r is subcritical and q is critical;(iv) Both q and r are critical.展开更多
We study the multiple existence of periodic solutions for a second-order non-autonomous dynamical systems (1). Using the method of invariant sets of descending flow and chain of rings theorem, we obtain the existence ...We study the multiple existence of periodic solutions for a second-order non-autonomous dynamical systems (1). Using the method of invariant sets of descending flow and chain of rings theorem, we obtain the existence of seven -periodic solutions.展开更多
文摘The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
文摘This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(u)u - beta integral (u)(0) g(s)ds is unbounded, a(x) is a Holder continuous function which changes sign on Omega and integral (Omega-) \a(x)\ dx is suitably small. The authors prove the existence of a nonnegative nontrivial solution for N > p > 1. in particular, the existence of a positive solution to the problem for N > p greater than or equal to 2. Our main theorem generalizes a recent result of Samia Khanfir and Leila Lassoued (see [1]) concerning the case where p = 2. They prove also that if g(u) = \u \ (q-2)u with p < q < p* and Omega (+) = {x is an element ofQ \a(x) > 0} is a nonempty open set, then the above problem possesses infinitely many solutions.
基金Supported by NSFC(Grant Nos.11771300 and 11726634)
文摘In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases:(i) Both q and r are subcritical;(ii) r is critical and q is subcritical;(iii) r is subcritical and q is critical;(iv) Both q and r are critical.
文摘We study the multiple existence of periodic solutions for a second-order non-autonomous dynamical systems (1). Using the method of invariant sets of descending flow and chain of rings theorem, we obtain the existence of seven -periodic solutions.
