A boundary value problem on the half-line for superlinear differential equations with changing sign weight

The existence of positive solutions x for a superlinear differential equation with p-Laplacian is here studied, satisfying the boundary conditions x(0) = x(∞) = 0. Under the assumption that the weight changes its sign from nonpositive to nonnegative, necessary and sufficient conditions for the existence are derived by combining Kneser-type properties for solutions of an associated boundary value problem on a compact set, a-priori bounds for solutions of suitable boundary value problems on noncompact intervals, and continuity arguments

Suitable classification of mortars from ancient roman and renaissance frescoes using thermal analysis and chemometrics

Background Literature on mortars has mainly focused on the identification and characterization of their components in order to assign them to a specific historical period, after accurate classification. For this purpose, different analytical techniques have been proposed. Aim of the present study was to verify whether the combination of thermal analysis and chemometric methods could be used to obtain a fast but correct classification of ancient mortar samples of different ages (Roman era and Renaissance). Results Ancient Roman frescoes from Museo Nazionale Romano (Terme di Diocleziano, Rome, Italy) and Renaissance frescoes from Sistine Chapel and Old Vatican Rooms (Vatican City) were analyzed by thermogravimetry (TG) and differential thermal analysis (DTA). Principal Component analysis (PCA) on the main thermal data evidenced the presence of two clusters, ascribable to the two different ages. Inspection of the loadings allowed to interpret the observed differences in terms of the experimental variables. Conclusions PCA allowed differentiating the two kinds of mortars (Roman and Renaissance frescoes), and evidenced how the ancient Roman samples are richer in binder (calcium carbonate) and contain less filler (aggregate) than the Renaissance ones. It was also demonstrated how the coupling of thermoanalytical techniques and chemometric processing proves to be particularly advantageous when a rapid and correct differentiation and classification of cultural heritage samples of various kinds or ages has to be carried out

On super-linear Emden–Fowler type differential equations

We study the second order Emden–Fowler type differential equation in the super-linear case. Using a Holder-type inequality, we resolve the open problem on the possible coexistence on three possible types of nononscillatory solutions (subdominant, intermediate, and dominant solutions). Jointly with this, sufficient conditions for the existence of globally positive intermediate solutions are established. Some of our results are new also for the Emden–Fowler equation

Positive decaying solutions for differential equations with phi-laplacian

We solve a nonlocal boundary value problem on the half-close interval $[1,\infty)$ associated to the differential equation $(a(t)\vert x^{\prime} \vert ^{\alpha} \operatorname {sgn}x^{\prime} )^{\prime }+b(t)\vert x\vert ^{\beta} \operatorname {sgn}x=0$ , in the superlinear case $\alpha<\beta$ . By using a new approach, based on a special energy-type function E, the existence of slowly decaying solutions is examined too

On Second-Order Differential Equations with Nonhomogeneous Φ-Laplacian

Equation with general nonhomogeneous Φ-Laplacian, including classical and singular Φ-Laplacian, is investigated. Necessary and sufficient conditions for the existence of nonoscillatory solutions satisfying certain asymptotic boundary conditions are given and discrepancies between the general and classical Φ are illustrated as well