In this paper, by using Leggett-Williams fixed-point theorem and Hölder inequality, we study the existence of three positive solutions for higher-order two-point boundary value problem (BVP):
This paper focuses on the study of the existence of a mild solution to time and space-fractional stochastic equation perturbed by multiplicative white noise. The required results are obtained by means of Sadovskii’s fixed point theorem.
We are concerned with positive solutions of two types of nonlinear elliptic boundary value problems (BVPs). We present conditions for existence, uniqueness and multiple positive solutions of a first type of elliptic BVPs. For a second type of elliptic BVPs, we obtain conditions for existence and uniqueness of positive global solutions. We employ mathematical tools including strictly upper (SU) and strictly lower (SL) solutions, iterative sequence method and Amann theorem. We present our research findings in new original theorems. Finally, we summarize and indicate areas of future study and possible applications of the research work.
"This paper deals with the existence, uniqueness and the multiplicity
of solutions for a class of fractional di erential equations boundary value prob-
lems involving three-point nonlocal Riemann-Liouville fractional derivative and
integral boundary conditions. Our results are based on some well-known tools of
xed point theory such as Banach contraction principle, xed point index theory
and the Leggett-Williams xed point theorem. As applications, some examples
are presented at the end to illustrate the main results."
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