# Ground state alternative for p-Laplacian with potential term

## Related Articles

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The work is the logical continuation of the works by N.M. Kukharchuk â€˜On solvability of the high-order quasi-linear elliptic equations in Râ„“â€™, â€˜Dissipative operators and nonlinear semigroups of compressions in Lp(Râ„“,dâ„“ x)â€™. It was established, that...

- Existence and Non-Existence Result for Singular Quasilinear Elliptic Equations. Mingzhu Wu; Zuodong Yang // Applied Mathematics;Nov2010, Vol. 1 Issue 5, p351
We prove the existence of a ground state solution for the qusilinear elliptic equation -div(âˆ£ âˆ‡u âˆ£p-2 âˆ‡u) =f (x,u) in Ï‰ âŠ‚ RN, under suitable conditions on a locally Holder continuous non-linearity f(x, t), the non-linearity may exhibit a singularity as t â†’...

- Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations. Zuodong Yang; Bing Xu // Boundary Value Problems;2007, p1
We consider the problem -div(âˆ£Î”uâˆ£P-2Î”u) = a(x)(um + Î»un),x ? RN,N â‰¥ 3, where 0 < m< p-1 < n,a(x) â‰¥ 0,a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists Î»0 > 0 such that the above-mentioned equation admits at...

- Construction of solutions of quasilinear parabolic equations in parametric form. Volosov, K. // Differential Equations;Apr2007, Vol. 43 Issue 4, p507
The article focuses on the construction of solutions of quasilinear parabolic equations in parametric form. The system of nonlinear algebraic equations for the derivatives has a unique solution which are treated as an overdetermined system for the functions that provides a solvability condition....

- Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces. Cavalheiro, Albo Carlos // Bulletin of the Belgian Mathematical Society - Simon Stevin;Feb2010, Vol. 17 Issue 1, p141
In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations -div [v(x)A(x, u, ?u)] + w(x)A0(x, u(x)) = f0 - ?j=1 nDjfj, on O in the setting of the weighted Sobolev spacesW01,p (O,w, ?).

- ON THE SMOOTHNESS OF SOLUTIONS OF ONE QUASILINEAR EQUATION IN R. Kukcharchuk, M. M.; Yaremenko, M. I. // Naukovi visti NTUU - KPI;2009, Vol. 2009 Issue 2, p148
We consider the smoothness of solutions of quasilinear elliptic partial differential equations. In this paper we develop the form method for proving the conditions of Minty-Browder's theorem, as well as for obtaining the research results on the smoothness of the solutions.

- Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems. El Manouni, Said; Perera, Kanishka // Boundary Value Problems;2007, p1
Using variational methods, we prove the existence and nonexistence of positive solutions for a class of (p,q)-Laplacian systems with a parameter.

- Existence of Multiple Positive Solutions of Quasilinear Elliptic Problems in â„N. Afrouzi, G. A.; Khademloo, S. // Advances in Dynamical Systems & Applications;2007, Vol. 2 Issue 1, p1
This paper concerns quasilinear elliptic equations of the form --div(|Î” u|p-2Î”u) = Î³a(x)u(x)|u|p-2(1-|u|Î» in â„N with p > 1 and a(x) changes sign. We discuss the question of existence and multiplicity of solutions when a(x) has some specific properties.

- Multiplicity solutions for a class of quasilinear critical problems in RN involving sign-changing weight function. Miotto, Márcio Luís // Revista CiÃªncia e Natura;2014, p367
In this paper, existence and multiplicity results to the following quasilinear critical problem ... are established, where Æ› > 0, 1 < q < p, with 2 â‰¤ p < N, p* = Np/N-p and the weight function Âƒ, among other conditions, can possibly change sign in RN. The study is based on...