Manuscript Topics

The subject of (local and nonlocal) boundary value problems is investigated in various scientific works due to the fact that they mathematically model a great number of natural phenomena, as e.g. heat conduction, fluid dynamics etc. Historically, several local boundary value problems were formulated for differential equations, where the response function depends only on the values of the function and its derivatives at a point. Latter on in such problems the response function depends on several delayed values of solution, or on some integral actions of them over an interval, while the variation of the solutions are ordinary derivative, or fractional and of simple or p-Laplacian type. On the other hand, originally, boundary conditions were of Neumann, or Dirichlet, or of mixed type, while latter on local or nonlocal type of boundary conditions were used. For the methods applied in the study of these problems the Banach contraction theorem is a good tool and to show existence of positive solutions the Guo-Krasnoselskii fixed point theorem in cones is mostly used and then follow the index theory, the Leray-Schauder Continuation Theorem, the Borsuk theorem for α condensing operators, and others.

The aim of this issue is to conduct a comprehensive up to date investigation into both local and nonlocal boundary value problems, especially, with the objectives described (and not limited to) as follows:
1) Sturm-Liouville differential systems with Neumann or Dirichlet boundary conditions,
2) Nonlinear boundary value problems with p-Laplacian, or Φ-Laplacian operator,
3) Periodic boundary value problems,
4) Multivalued boundary value problems,
5) Boundary value problems with integral boundary conditions,
6) Singular nonlinear boundary value problems for second order differential equations,
7) Multiple nonnegative solutions of nonlinear boundary value problems,
8) Positive solutions for m-point boundary value problems,
9) Functional boundary value problems for functional differential equations of ordinary or neutral type,
10) Boundary value problems for nonlinear equations in Banach spaces.
11) Boundary value problems in abstract spaces,
12) Boundary value problems of fractional type.
Keywords: Multi-parameter boundary value problems; Indefinite weight; Multipoint boundary value problems; Nonlinear boundary value problems; Singular nonlinear boundary value problems; Positive solutions; Fractional derivative; Impulses.

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