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In fact, suppose that there exists a positive solutions sequence of (1.1) and such that as.
Under the assumptions (H1 - H3), x is a positive solutions of BVP (1.1) if and only if x is a fixed point of A in K.
We know that ( u, v ) is a positive solutions of system (1.1) if and only if ( u, v ) is a fixed point of T in K. Lemma 2.6 Assume that ( H 0 ), ( H 1 ) hold.
Obviously, ((u,v)) is a positive solutions of the boundary value problem (1.1 - 1.2 1.1 - 1.2nly if ((u,v)) is andixed ponly of T if (Psetminus {(0,v) }).
end{aligned} Obviously, ((u,v)) is a positive solutions of the coupled boundary value problem (1.1) and (1.2) if and only if ((u,v)) is a fixed point of T in (Psetminus{ 0,0)}).
In [18 21], the authors studied the existence of a positive solutions of two types of systems for nonlinear fractional differential equations left { textstylebegin{array}l} D_{0+}^{alpha}u(t)+lambda f t,u(t),v(t))=0,quad tin 0,1), D_{0+}^{beta}v(t)+mu g t,u(t),v(t))=0,quad tin 0,1), end{array}displaystyle right.
Similar(54)
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com