On the existence of a nontrivial solution to nonlinear problems at resonance

Existence and Multiplicity of Solutions for a Class of Semilinear Elliptic Equations

“…Remark 2 There are functions f x t satisfying our Theorem 2 and not satisfying those in [2,12,21]. In fact, let…”

“…In [2,12,21] some multiplicity theorems are obtained by using the topological degree technique and the variational methods, respectively. Except for [7,14], the linear case is only treated.…”

Remarks on existence and multiplicity of solutions for a class of semilinear elliptic equations

“…The existence results are given for problem (1) in [1][2][3][4][5][9][10][11][12][13][14][15][16][17][18][19]23]. In [5][6][7][8] some multiplicity theorems are obtained by using the topological degree technique and the variational methods, respectively. Except for [1,2,23], the linear case is only treated.…”

Solutions of elliptic problems with nonlinearities of linear growth

“…For examples, the elliptic resonance problems with unbounded perturbations were studied in [39,40] using Morse theory and in [32] via the flow invariant set method. We mention that the strong resonance problems were studied by , Capozzi-Lupo-Solimini [10], Chang-Liu [13], and Li-Wang [30]. There were also works to remove additional resonance conditions from former results for problems with resonance at exactly one eigenvalue of the Laplacian operator.…”