Abstract. In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais{Smale sequences of a strongly indenite functional. The abstract result will be used to study the semilinear Schrödinger equation −u + V (x)u = K(x)juj2−2u+ g(x, u), u 2 W 1,2(RN), where N 4; V,K, g are periodic in xj for 1 j N and 0 is in a gap of the spectrum of − + V; K> 0. If 0 < g(x, u)u cjuj2 for an appropriate constant c, we show that this equation has a nontrivial solution. Mathematics Subject Classication. 35B33, 35J65, 35Q55. Received October 28, 2002
In this paper, we study a nonlinear Schrodinger equation with periodic potential. We assume that zer...
Abstract. We show that the problem at critical growth, involving the 1-Laplace op-erator and obtaine...
We establish the existence of a nontrivial weak solution to strongly indefinite asymptotically linea...
Abstract. We consider the semilinear Schrödinger equation −∆u + V (x)u = K(x)|u|2 −2u + g(x, u), u ...
To Professor Kazimierz Gęba on the occasion of his 70th birthday Abstract. We consider the semilinea...
AbstractSome parameter-depending linking theorems are established, which allow to produce a bounded ...
We consider the semilinear Schrödinger equation $$ -\Delta_A u+V(x)u =Q(x)|u|^{2^{*}-2}u. $$ Assu...
In this work, we present an abstract linking theorem for Cerami sequences, but without using the Cer...
The main purpose of this paper is to establish the existence of a solution of the semilinear Schr¨od...
We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an...
In this work, we study issues related the existence, nonexistence and regularity of solutions to se...
In this thesis we study the existence of solutions for a class of semilinear Schr¨odinger equations ...
AbstractWe consider the equation −Δu+V(x)u−k2(Δ(|u|2))u=g(x,u), u>0, x∈R2, where V:R2→R and g:R2×R→R...
We show the existence of a nonzero solution for the semilinear Schrodinger equation $-\Delta u+V(...
We show the linking-type result which allows us to study strongly indefinite problems with sign-chan...
In this paper, we study a nonlinear Schrodinger equation with periodic potential. We assume that zer...
Abstract. We show that the problem at critical growth, involving the 1-Laplace op-erator and obtaine...
We establish the existence of a nontrivial weak solution to strongly indefinite asymptotically linea...
Abstract. We consider the semilinear Schrödinger equation −∆u + V (x)u = K(x)|u|2 −2u + g(x, u), u ...
To Professor Kazimierz Gęba on the occasion of his 70th birthday Abstract. We consider the semilinea...
AbstractSome parameter-depending linking theorems are established, which allow to produce a bounded ...
We consider the semilinear Schrödinger equation $$ -\Delta_A u+V(x)u =Q(x)|u|^{2^{*}-2}u. $$ Assu...
In this work, we present an abstract linking theorem for Cerami sequences, but without using the Cer...
The main purpose of this paper is to establish the existence of a solution of the semilinear Schr¨od...
We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an...
In this work, we study issues related the existence, nonexistence and regularity of solutions to se...
In this thesis we study the existence of solutions for a class of semilinear Schr¨odinger equations ...
AbstractWe consider the equation −Δu+V(x)u−k2(Δ(|u|2))u=g(x,u), u>0, x∈R2, where V:R2→R and g:R2×R→R...
We show the existence of a nonzero solution for the semilinear Schrodinger equation $-\Delta u+V(...
We show the linking-type result which allows us to study strongly indefinite problems with sign-chan...
In this paper, we study a nonlinear Schrodinger equation with periodic potential. We assume that zer...
Abstract. We show that the problem at critical growth, involving the 1-Laplace op-erator and obtaine...
We establish the existence of a nontrivial weak solution to strongly indefinite asymptotically linea...