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

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