Multiple Solutions of p-Laplacian with Neumann and Robin Boundary Conditions for Both Resonance and Oscillation Problem
نویسندگان
چکیده
We discuss Neumann and Robin problems driven by the p-Laplacian with jumping nonlinearities. Using sub-sup solutionmethod, Fucı́k spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equations with Robin boundary and obtain infinitely many nontrivial solutions.
منابع مشابه
Nonexistence and existence results for a 2$n$th-order $p$-Laplacian discrete Neumann boundary value problem
This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.
متن کاملA Collocation Method with Modified Equilibrium on Line Method for Imposition of Neumann and Robin Boundary Conditions in Acoustics (TECHNICAL NOTE)
A collocation method with the modified equilibrium on line method (ELM) forimposition of Neumann and Robin boundary conditions is presented for solving the two-dimensionalacoustical problems. In the modified ELM, the governing equations are integrated over the lines onthe Neumann (Robin) boundary instead of the Neumann (Robin) boundary condition equations. Inother words, integration domains are...
متن کاملExistence solutions for new p-Laplacian fractional boundary value problem with impulsive effects
Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...
متن کاملExistence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملINFINITELY MANY SOLUTIONS FOR A CLASS OF P-BIHARMONIC PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS
The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.
متن کامل