Positive solutions for some 1-dimensional boundary value problems of Laplace-type
Tóm tắt
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type
$$\left( {\phi (x'(t))} \right)^\prime + q(t)f(t,x(t),x'(t)) = 0, t \in (0,1),$$
subject to the following boundary condition:
$$a_1 \phi (x(0)) - a_2 \phi (x'(0)) = 0, a_3 \phi (x(1)) + a_4 \phi (x'(1)) = 0,$$
where ϕ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.
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