In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be un- bounded by making use of the M...In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be un- bounded by making use of the Morse theory for a C^2-function at both isolated critical point and infinity.展开更多
In this paper,we consider the inverse resonance problems for the discontinuous and non-selfadjoint Sturm-Liouville problem.We prove the uniqueness theorem and provide a reconstructive algorithm for the potential by us...In this paper,we consider the inverse resonance problems for the discontinuous and non-selfadjoint Sturm-Liouville problem.We prove the uniqueness theorem and provide a reconstructive algorithm for the potential by using the Cauchy data and Weyl function.展开更多
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.
We are concerned with the following Dirichlet problem: -△u(x) = f(x, u), x ∈ Ω. u ∈ H_0~1(Ω). (P) where f(x, t) ∈ C(Ω×R), f(x, t)/t is nondecreasing in t ∈ R and tends to an L~∝-function q(x) uniformly ...We are concerned with the following Dirichlet problem: -△u(x) = f(x, u), x ∈ Ω. u ∈ H_0~1(Ω). (P) where f(x, t) ∈ C(Ω×R), f(x, t)/t is nondecreasing in t ∈ R and tends to an L~∝-function q(x) uniformly in x ∈ Ω as t→+∝ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case. an Ambrosetti-Rabinowitz-type condition, that is. for some θ>2. M>0, 0<θF(x. s)≤ f(x, s)s, for all |s|≥M and x ∈ Ω, (AR) is no longer true, where F(x, s) = integral from n=0 to s f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming (AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable, conditions on f(x, t) and q(x). Our methods also work for the case where f(x, f) is superlinear in t at infinity. i.e., q(x) ≡∞.展开更多
文摘In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be un- bounded by making use of the Morse theory for a C^2-function at both isolated critical point and infinity.
基金supported in part by the National Natural Science Foundation of China (11871031)the Natural Science Foundation of the Jiangsu Province of China(BK 20201303)supported in part by Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX20 0245)
文摘In this paper,we consider the inverse resonance problems for the discontinuous and non-selfadjoint Sturm-Liouville problem.We prove the uniqueness theorem and provide a reconstructive algorithm for the potential by using the Cauchy data and Weyl function.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.
文摘We are concerned with the following Dirichlet problem: -△u(x) = f(x, u), x ∈ Ω. u ∈ H_0~1(Ω). (P) where f(x, t) ∈ C(Ω×R), f(x, t)/t is nondecreasing in t ∈ R and tends to an L~∝-function q(x) uniformly in x ∈ Ω as t→+∝ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case. an Ambrosetti-Rabinowitz-type condition, that is. for some θ>2. M>0, 0<θF(x. s)≤ f(x, s)s, for all |s|≥M and x ∈ Ω, (AR) is no longer true, where F(x, s) = integral from n=0 to s f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming (AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable, conditions on f(x, t) and q(x). Our methods also work for the case where f(x, f) is superlinear in t at infinity. i.e., q(x) ≡∞.
