Singular and regular second order φ-Laplacian equations on the half-line with functional boundary conditions

Asymptotic properties of PDEs in compact spaces

“…On the other hand, the study of ODEs on unbounded domains has progressed steadily [10,13,[33][34][35]. The key to deal with unbounded domains is to use some kind of relatively compactness criterion such as [37, Theorem 1]see for instance [9,37].…”

Existence of Solutions of Integral Equations Defined in Unbounded Domains Via Spectral Theory

“…When working with integral problems defined in unbounded intervals, the main difficulty is the lack of compactness of the operator. In the recent literature (see [4,6,[12][13][14]), most of the authors use the following relatively compactness criterion (see [3,16]) to deal with this problem: 1 ([16, Theorem 1]). Let E be a Banach space and ( , E) the space of all bounded continuous functions x : → E. For a set D ⊂ ( , E) to be relatively compact, it is necessary and sufficient that:…”

Multiple solutions for mixed boundary value problems with phi-Laplacian operators

“…Existence of solutions for boundary value problems can be studied by different methods:fixed point theorems, topological degree, fixed point index theory, lower and upper functions, etc. ; for bounded intervals see for example [1,2,3,4,7,8,9] and for unbounded intervals [5,6] and the reference therein. In particular, using the method of upper and lower solutions and the fixed point index theory the authors in [9] obtained existence and multiplicity results of solutions for the Dirichlet boundary value problem.…”