and Applied Analysis 3 B∞ There is h ∈ C Ω,R such that ∣∣f x, z ∣∣ ≤ h x , ∀ x, z ∈ Ω × R2, ∣∣g x, z ∣∣ ≤ h x , ∀ x, z ∈ Ω × R2. 1.8 Under these hypotheses, system 1.1 is asymptotically quadratic at infinity due to the presence of a linear part given by the function A ∈ S2 Ω . In addition, when λk A 1 for some k ≥ 1 the problem 1.1 becomes resonant. In this case, in order to obtain existence an...

This article concerns the existence and multiplicity of positive solutions for the singular Sturm-Liouville boundary value problem (p(t)u′(t))′ + h(t)f(t, u(t)) = 0, 0 < t <∞, au(0)− b lim t→0+ p(t)u′(t) = 0, c lim t→∞ u(t) + d lim t→∞ p(t)u′(t) = 0. We use fixed point index theory to establish our main results based on a priori estimates derived by utilizing spectral properties of associated l...

Line intensity mapping (LIM) proposes to efficiently observe distant faint galaxies and map the matter density field at high redshift. Building upon formalism in companion paper, we first highlight degeneracies between cosmology astrophysics LIM. We discuss what can be constrained from measurements of mean redshift-space power spectra. With a sufficient spectral resolution, large-scale distorti...

and Applied Analysis 3 The rest of the paper is organized as follows: in Section 2, we state the main results of problem (7). In Section 3, we provide some preliminary results, and the proofs of the main results together with several technical lemmas are given in Section 4. The final section of the paper contains an example to illustrate the theoretical results. 2. Main Results In this section,...