Partial Differential Equations 2

TL;DR: In this article, the multiplicity and concentration of positive solutions for the semilinear Kirchhoff type equation were studied and the relation between the number of positive ground state solutions and the topology of the set of the global minima of the potentials by minimax theorems and the Ljusternik-Schnirelmann theory was investigated.

TL;DR: In this article, the authors provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e., when the option has an arbitrary payoff function and depends on the path of the asset price process.

TL;DR: In this paper, the singular boundary value problem was considered and the exact result for λ ⁎ ( Ω, p, γ, h ) was obtained for all λ ∈ ( 0, λ ΁) and no solution for ΁ > ΁.

TL;DR: In this paper, a class of Kirchhoff type problems with singularity and nonlinearity was studied and the uniqueness and existence of positive solutions of those problems by variational methods were obtained.