The object of research is the Fučik spectrum for (p,q)-Laplacian operator. In present paper, we are going to introduce notion a non-linear, non-homogeneous operator, which operator through study following eigenvalue boundary problem: {–∆pu–∆qu=λ(u+)p–1–μ(u–)q–1 in Ω, u=0 on ∂Ω, where Ω⊂RN, N≥1 bounded open subset with smooth and λ μ two real parameters. order establish show existence non-trivia...

Under certain nonlinear growth conditions of the nonlinearity, we investigate the existence of solutions for a nonlinear Hadamard type fractional differential equation with strip condition and p-Laplacian operator. At the end, two examples are given to illustrate our main results. ©2016 All rights reserved.

Let T be a time scale. We study the existence of three positive solutions for the nonlinear four-point singular boundary value problem with p-Laplacian operator on time scales. Some new results are obtained for three positive solutions by applying Leggett-Williams fixed-point theorem in a cone, which is different from the previous. Mathematics Subject Classification: 34B16

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). Using variational techniques based on the smooth critical point theory and the second deformation theorem, we prove an existence theorem and a multiplicity theorem, under hypothesis that in general do not imply the coercivity of the Euler functional.

In this paper, we study the existence of positive solutions for nonlinear four-point singular boundary-value problems for higher-order equation with the p-Laplacian operator. Using the fixed-point index theory, we find conditions for the existence of one solution, and of multiple solutions.

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

This paper aims to investigate the existence of solutions for fractional integral boundary value problems with p(t)-Laplacian operator. By using the fixed point theorem and the coincidence degree theory, some new results are obtained, which enrich existing literatures. Some examples are supplied to verify our main results.

In this work we give necessary and sufficient conditions for having a maximum principle for cooperative elliptic systems involving p-Laplacian operator on the whole RN . This principle is then used to yield solvability for the cooperative elliptic systems by an approximation method.

In this paper, we prove the existence of at least two nontrivial solutions for a nonlinear elliptic problem involving p(x)-Laplacian-like operator and nonsmooth potentials. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.