Volume 35 • Number 2 • 2012   • The Existence of Three Positive Solutions to Integral Type BVPs for Second Order ODEs with One-Dimensional $p$-Laplacian Yuji Liu Abstract. This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional $p$-Laplacian $$ \left\{\begin{array}{l}[\rho(t)\Phi(x'(t))]'+f(t,x(t),x'(t))=0,\quad t\in (0,1),\\ \phi_1(x(0))=\int_0^1g(s)\phi_1(x(s))ds,\\ \phi_2( x'(1))=\int_0^1h(s)\phi_2(x'(s))ds.\end{array}\right.$$ Sufficient conditions to guarantee the existence of at least three positive solutions of this BVP are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional $p$-Laplacian term $[\rho(t)\Phi(x'(t))]'$ involved with the function $\rho$, which makes the solutions un-concave. 2010 Mathematics Subject Classification: 34B10, 34B15, 35B10, 65L10. Full text: PDF