Existence of solutions for some boundary value problems of fractional \(p\)-Laplacian equation at resonance (Q372711): Difference between revisions

The paper is concerned with the existence of solutions of the following two boundary value problems for \(p\)-Laplacian differential equations at resonance: \[ D_{0^+}^\beta\phi_p(D_{0^+}^\alpha x(t))=f(t,x(t),D_{0^+}^\alpha x(t)),\quad t\in[0,1], \] \[ x(0)=0,\quad D_{0^+}^\alpha x(0)=D_{0^+}^\alpha x(1); \] and \[ D_{0^+}^\beta\phi_p(D_{0^+}^\alpha x(t))=f(t,x(t),D_{0^+}^\alpha x(t)),\quad t\in[0,1], \] \[ x(1)=0,\quad D_{0^+}^\alpha x(0)=D_{0^+}^\alpha x(1). \] The main tool is the coincidence degree theory. An example is given as an application of their results.