arXiv subjects

Baoxia Qin

Publications and source records attributed to Baoxia Qin.

4 recordsLinked to original sources

arXiv2026

Abstract Indefinite Problems in Riesz Spaces with Its Applications

This paper investigates the existence of critical points for functionals defined on a Hilbert space $X$ which is continuously embedded into a Banach lattice $E$. A lattice decomposition of $E$ is constructed, which possesses both order disjointness and inner-product orthogonality. Accordingly, a corresponding decomposition of the Hilbert space $X$ is obtained. Under this decomposition, the associated functional satisfies the energy collapse condition and order-preserving property on certain subspaces, while exhibiting coerciveness on others. By combining the descending flow invariant set method with Morse theory, we establish the existence of multiple critical points for the abstract indefinite problems. Finally, applications to elliptic boundary value problems are provided.

math.FA↗

arXiv2026

Solutions for Strongly Monotone Operator Equations in Riesz Spaces

This paper is devoted to the study of solutions for a class of operator equations governed by strongly monotone operators on real Riesz spaces continuously embedded into Banach lattices. By exploiting the intrinsic lattice structure of Banach lattices, we establish refined growth assumptions on nonlinear terms to guarantee that suitable neighbourhoods of positive and negative cones are invariant under the descending flow. Combining the descending flow invariant set technique with the theory of strongly monotone operators, we derive abstract existence theorems: the operator equation possesses at least one positive solution, one negative solution and one sign-changing solution. These abstract results are further applied to $(p,q)$-Laplacian boundary value problems, yielding corresponding multiplicity conclusions on positive, negative and sign-changing solutions.

math.FA↗

arXiv2024

The Method of Invariant Sets of Descending Flow for Locally Lipschitz Functionals

In this paper, we extend the method of invariant sets of descending flow that proposed by Sun Jingxian for smooth functionals to the locally Lipschitz functionals. By this way, we obtain the existence results for the positive, negative and sign-changing critical points of the locally Lipschitz functionals, and apply these theoretical results to the study of differential inclusion problems with p-Laplacian. In order to obtain the above results,we develop some new techniques: 1) We establish the method of how to extend the pseudo-gradient field to the whole space on the premise of preserving the useful information of the local pseudo-gradient field; 2) In the case of set-valued mapping, a pseudo-gradient field is established to make both the cone and the negative cone being invariant sets of descending flow. To obtain our main results, a new class of (PS) condition is also proposed.

math.AP↗

arXiv2024

Sign Changing Critical Points for Locally Lipschitz Functionals

In this paper, some existence results for sign-changing critical points of locally Lipschitz functionals in real Banach space are obtained by the method combining the invariant sets of descending ow method with a quantitative deformation. First we assume the locally Lipschitz functionals to be outwardly directed on the the boundary of some closed convex sets of the real Banach space. By using the relation between the critical points on the Banach space and those of the closed convex sets, we construct a quantitative deformation lemma, and then we obtain some linking type of critical points theorems. These theoretical results can be applied to the study of the existence of sign-changing solutions for differential inclusion problems. In contrast with the related results in the literatures, the main results of this paper relax the requirement that the functional being of C1 continuous to locally Lipschitz.

math.AP↗