| Abstract: |
| This work is concerned with the existence of two nontrival positive solutions to a class of boundary value problem (BVP), involving a $p$-Laplacian, of the form
\begin{align*}
(\Phi_p(x^{`}))^{`} + g(t)f(t,x) & = 0, \quad t \in (0,1),\
x(0)-ax^{`}(0) & = \alpha[x],\
x(1)+bx^{`}(1) & = \beta[x],
\end{align*}
where $\Phi_{p}(x) = |x|^{p-2}x$ is a one dimensional $p$-Laplacian operator with $p>1, a,b$ are real constants and $\alpha,\beta$ are given by the Riemann-Stieltjes integrals
\[ \alpha[x] = \int \limits_{0}^{1} x(t)dA(t), \quad \beta[x] = \int \limits_{0}^{1} x(t)dB(t),\]
with $A$ and $B$ are function of bounded variations. The approach is based on the fixed point index theory. |
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